The Avatar of Khaine in its natural state of existence: dying horribly to make the character or faction GW is trying to show off look awesome.
Khaela Mensha Khaine AKA Khaine, the Bloody-Handed God is the Dark Elf, High Elf, and Eldar God of War and Fire.
Khaine is one of the last living Eldar Gods after the fall of the Eldar, although due to him being trampled on and pushed into realspace when Khorne was busy piledriving baby Slaanesh all over Eldar heaven, he's no longer "alive" in a spiritual sense and is now shattered into a bajillion pieces. These pieces made their way into the Craftworlds, where they can be used to summon the Avatar of Khaine when the time comes. An Avatar is a towering daemonic creature that makes anything it can get its hands on shit bricks. He's also the angriest god of the Eldar Pantheon, and while he can't really contest with the likes of Angron and Doombreed, he probably comes close.
 The story of the single angriest Eldar entity ever
Long ago when the Eldar were the most powerful race in the universe and they hadn't raped the entire universe yet, Khaine heard from Lileath, the prophesy giver of the Eldar pantheon, that the Eldar will one day kill him. Khaine decided to murder every last one of the pansies to ensure that never happened. However Isha, the mother of the Eldar, cried for the Eldar race because no sane mother would want her own children butchered to death by a maniacal god of war.
Then Asuryan, the Phoenix King, intervened and decided to spare the Eldar from being killed by Khaine, and Isha from having to see it, by creating a barrier to separate mortals from gods for all eternity, ensuring the mortal Eldar would never have the chance to kill Khaine, nor would Khaine get the ability to go down to the mortal realm and kill all of the Eldar. This worked for Khaine, but not so well for Isha.
Isha missed talking to her children and so cheated through the whole barrier deal by having Vaul the Artificer (The best craftsman of the Eldar gods) make spirit stones to communicate with them. Khaine however, discovered this, and cried foul on Isha and her husband Kurnous. Asuryan, not wanting to look like a biased dick, told Khaine that he could do whatever he wanted with the two, which equated to eternal torture at the hands of Khaine. Vaul got pissed at this and bargained with Khaine that he would make a hundred of his finest swords in a year in exchange for Isha and Kurnous' release, which he agreed to.
However, because Vaul decided to jerk off on the last day rather than work, he couldn't make the last sword in time and instead tried to trick Khaine out of the deal by putting one normal sword in the bunch of 99 epic swords he made, thinking that with Khaine's short attention span and his inability to count beyond 10, he won't notice and just accept the fuckheug pile of swords as is. He however didn't count on Khaine to be a total mathfag/detailfag whenever he's weaponwhoring and so Khaine got almighty pissed over this and fucked over Vaul by beating the shit out of him and subsequently chained to him an anvil when he discovered the single normal sword amongst the bunch. Yeah, a lot of people reeeaaallly love to screw with Khaine, too bad the guy has a terrible sense of humor.
Then he murdered Eldanesh, an Eldar champion, in an unspecified incident that had Asuryan condemn him to have blood eternally drip from his hands to remind him of his crime, which also earned him the title "Khaela Mensha".
Then, when Slaanesh was born because of the Eldar's planetary system-wide orgies, Khaine tried to fight the newly-born god and managed to fight Slaanesh despite the herm having the power of the other gods in the pantheon and countless Eldar souls. After lord knows how long he was beaten and about to be devoured, but then Khorne came out and challenged Slaanesh to a battle, as he claimed that Khaine was his property and so Slaanesh had no right to eat him. Needless to say, Slaanesh lost. While Khorne was busy piledriving and backbreaking Slaanesh into oblivion, Khaine was in the middle of this and got shattered into a million pieces, presumably because Khorne left his axe back at his Brass Citadel and Khaine was the only available melee weapon at the time, or maybe he made a fine object to drop Slaanesh on over and over again. The rest is history.
So in the end, Lileath's prophesy did come true in a sense. The Eldar were responsible for the birth of Slaanesh, which sort of killed him, but not totally because technically he is still "alive", it's just that he's not up and about anymore like Cegorach and Isha, but has to live with the fact that he, the Eldar god of war,
got beaten and raped by a hermaphrodite for a God is probably a fate worse than death. Khorne's intervention caused Khaine to shatter into little bits, which considering that he was in the middle of fighting Slaanesh seems perfectly acceptable. Either way, it was either Just As Planned by Tzeentch who was the only Chaos God who didn't directly intervene during the fall of the Eldar, or Cegorach because that hilarious son of a bitch just HAD to do it for all what Khaine's done in Eldar heaven before he slipped back into the Webway. Hell, for all we know, the two could have orchestrated the entire fall of the Eldar just to be the only 2 entities who managed to successfully screw with Khaine and get away with it.
 The Avatar of Khaine
The Avatar of Khaine is a unique Eldar daemon unit. The Avatar is basically, a small fragment of Khaine's power given form (although small is very relative; an Avatar is about as powerful as a Greater Daemon of Chaos.) through one of his fragments present in a Craftworld.
The Eldar will only summon the Avatar into battle under the most dire of circumstances where there is no other choice. This is because in order to summon the Avatar, the Eldar must sacrifice one of their Exarchs, known as the "Young King", in order to bring him into existence, which only lasts for a limited amount of time. Much like any daemon, after some time, the Avatar will eventually degenerate and disappear, taking the sacrificed Exarch with it.
On the tabletop, this thing has gone from having its stats rolled randomly to being a dedicated melee monstrous creature which has the notable ability of immunity to flamer and melta weapons, because Khaine is also the Eldar god of fire. Although there are multiple Avatars, since each Craftworld only has one, it's considered a special character. In the current codex, it's mostly overshadowed by other HQs due to its cost.
He used to be really strong, but Games Workshop's authors have taken a liking to murdering Avatars every chance they get.
- Killed hilariously by Marneus Calgar in hand-to-hand combat in the 5th ed "Space Marine" codex (after sweeping through a Devastator and Terminator squad, but still).
- Possessed by a Keeper of Secrets (oh irony). How is that even possible? It doesn't have a body or soul to possess! (It wasn't "alive" at the time if that helps)
- Trampled to death by twelve stampeding carnifexes during the battle between Craftworld Iyanden and the Hive Fleet Kraken. What happened was that the Avatar goaded the swarm's Hive Tyrant into a duel. What the Avatar failed to realize that this wasn't tabletop and that the Tyranids are a pragmatic instead of an idealistic lot who have no concept of honorable or dirty fighting, so the Hive Tyrant just raised his brow at this and sent twelve Carnifexes to run the Avatar over. (Ironically Matt Ward gave him a more dignified death).
- Strangled(WTF?)/Neck snapped by Fulgrim. Which doesn't make much since considering it neither breathes nor has bones. Then again, Astartes (and humanity in general) have proven time and again that they can kill anything, all thanks to plot armor brought to you by Games Workshop.
- Killed by the Sanguinor. To be fair, the Sanguinor is (probably) literally Sanguinius reborn sooo... yeah.
- "Put out of his misery" by Lorgar Aurelian (who was at the time considered to be the worst fighter out of all the Primarchs). Though Avatar was heavily damaged even before the fight, unable to even stand and driven mad by centuries spent in Warp, and just few pages before Lorgar proved to be top level badass as he battled and bested Anggrath, the uberbloodthirster of Khorne who can eat Avatars and Titans like cookies.
- Killed by Gabriel Angelos' 3rd company without the aid of anything heavier than a Dreadnought during the Tartarus Campaign (though video game examples are slightly less ridiculous because it's usually up to the player rather than their plot armor).
- Killed in a break-dancing competition by a Khornate Bloodthirster during the Eldar's incursion on Lorn V (at least this one's non-canon).
- Killed in single combat by Epistolary Anteas of the Blood Ravens during the Kronus Campaign. (Yep, Papa Smurf himself just got outdone by a Librarian).
- This might not be entirely canon; Anteas is only credited with stealing the pieces of the Avatar's armor, and the in-game Librarian is only fighting the Avatar single-handed because of engine limitations (the cutscene is designed to show off monstrous creatures, which Spess Mehreens don't have).
- Killed twice by Force Commander Hair Gel's squad during the fighting to pacify the Eldar in subsector Aurelia. Though to be honest, both of these battles are really fucking hard if you don't have a well-managed squad, and nothing short of greater daemons is more than a speedbump for Tarkus or Cyrus.
- Stabbed in the heart by Maugan Ra to temper his Maugetar. Even in his own faction, the guy gets killed anticlimactically.
- Abandoned on a Maiden World, where its connection to the Eldar was severed, reducing it to a mindless state of rage. The now-unbound Avatar consequently called out to the Orks of the nearby Octarius system, which were happy to answer it. It's kind of sad that the only time the Avatar isn't being a jobber is when he's being used by someone else entirely.
- Killed by the Legion of the Damned when assisting the Invaders in their assault on Craftworld Idharae. When the Legion realized their flaming bolters did squat against the Avatar, they instead brought the roof down on it. Bringing down the roof...sigh...
Similar to his 40k part only not in pieces. He is given a LOT more respect in this version of him, shown to be a powerful, mighty god that is renowned and feared (as he should be you pussys).
There was no prophesy that the Elves would harm him, so that 40k story about him trying to wipe the mortal elves out didn't happen in the Fantasy universe because he had no reason to dislike the mortal elves. The Swords of Vaul story DID happen however, and that final Sword was the Widowmaker which somehow ended up in the mortal world (a lot of Khaine's shit does actually, probably at a 1:1 ratio with Lileath's). He's not outright evil (other than the fact he likes war just like the Fantasy players), rather he's pretty neutral and the High Elves love to acknowledge the dualities of "evil has to be killed by good, there can be no joy without sorrow, etc" with him.
Overall, Khaine is a huge asshole and High Elves acknowledge him as part of the pantheon but do not actually worship him (barring a small minority amongst the Nagarythe who are a bit more fucked up than the rest of the lot, which is saying something). Dark Elves on the other hand praise him in Asuryan's place (when they aren't worshiping Slaanesh anyway.
High Elves do not insult him however, and still include a depiction of him amongst the High Elf Pantheon. The Shrine of Khaine is a hotly fought over place between the High and Dark Elves, the former trying to prevent his worship and the latter trying to, well, worship at it. It's the location of the Widowmaker (see below).
He's not overly fond of ANY of the elf races in the mortal world, but since the Dark Elves revere him instead of big boss Asuryan (Eldar confirmed for Dark Elves, Dark Eldar confirmed for
badass Dark Elves *FWIP* TRAITOR, DIE IN THE NAME OF OUR LORD ASURYAN AND THE PHOENIX KING!) he grants them boons then sits back with some popcorn and watches the Elves slaughter each other.
 The Sword of Khaine
Long ago, when the Old Ones left and Daemons were overrunning the world, Aenarion, the first Phoenix King of the High Elves (as well as the father of the king of the Dark Elves) took up the Sword to help fight off the Daemons. He used it to kick so much ass he eventually drove the Daemons back. During the final battle against the Daemons, while his best bud created a Vortex to syphon off the extra magic and keep the Daemons from manifesting properly, he used the sword to fight and kill all four avatars of the Chaos Gods all on his own. Suck it Marneus.
Aenarion, mortally wounded, took his (also mortally wounded) dragon and flew across half a continent (which, thanks to the size of the Warhammer world, means a full sized continent) back to the island then stuck it in the ground at the Shrine, where it remains to this day.
Some editions imply the Widowmaker being grabbed by Aenarion and thus causing the Dark Elves to happen is Khaine's plan come to fruition so there'd always be elves fighting and thus his portfolio would mean something. Other times, he's with the other gods in facepalming when he nabbed it and cursed himself. It's open to interpretation.
Dark Elf Cauldron of Blood, a mobile shrine to Khaine administered to by his fangirls.