Eldar
The Eldar (aka Space Elves aka Fairies) are one of the "playable" armies in Warhammer 40,000. They are essentially elves ported directly from Tolkien into space, pointy ears and all, and as a result are often called Elfdar by fa/tg/uys. They have very advanced technology, but ages of warfare and strife have reduced their population from great empires in the past to the few surviving Craftworlds or Maiden Worlds still present in the 41st Millennium.
In the 40k game, the Eldar army is comprised of specialized units that excel at a particular task, as opposed to more general all-rounders like the Space Marine tactical squads. Their vehicles are almost all hovercraft, excepting War Walkers, which are (unsurprisingly) walker vehicles. The Eldar also have a few special tricks up their elfy sleeve. This comes in the form of the wraithlord(a giant ghost warrior in a giant wraithbone structure. It's like a space marine dreadnought in purpose: They both have a dead guy thingy in them) and the avatar.(It's like a giant monster made of lava. This is completely unrelated to the movie.)
In spite of their fall from being a colossal empire that ruled when Mankind was still poking things with sticks and roasting dead animals over the fire in caves to their current state (a dying race slowly being whittled down by combat losses and Slaanesh), the hubris of the Eldar, and their legendary disdain for every single bit of non-Eldarin life remains completely unchanged, and the race as a whole has a superiority complex that would put Failbaddon to shame. They often act indirectly, subtly manipulating other races (most commonly the Imperials) into doing what they want in a proud emulation of one of the galaxy's biggest dicks. These traits, paired with their being used as the defenders of the status quo (see below) and the blatant favoritism they generally recieve from any work featuring them (this for example) have caused them to be the single most-hated race by /tg/, putting even the fucking Weeaboo Space Communists and Space Zombies to shame.
Recently the Eldar seemed to have become the whipping boys of GW. You know they hate you when you can't even win in your own codices. Also, almost every victory they get nowadays is a Pyhrric one, which is considered on /tg/ to be proof that things are progressing in a better direction given the Eldar tendency to be a status quo fia for fluffwriters.
History
The Eldar were one of many races created by the Old Ones to fight against the Necrons. They were made to be powerful psykers to take advantage of the C'tan's weakness to the powers of the Warp. At the height of their civilization, approximately the same time humans were starting to evolve, they used their advanced technology to perform pretty much all work required and devoted themselves to pursuing lives of hedonistic decadence. Some Eldar decided to forsake the ways of their kin and left to settle other planets at the fringes of the galaxy; this turned out to be a pretty smart move, since the planet-wide orgies going on back home created the Eye of Terror and caused the birth of the Chaos God Slaanesh, coincidentally resulting in the deaths of most of the Eldar still on their homeworlds. Thus securing the Eldar's status as the worst fappers in the galaxy.
The Eldar present in the 41st millennium are the descendants of those who left to settle other planets or are the mercentile group that travelled around in their enormous ships called Craftworlds. They are dedicated to their fight against the forces of Chaos spawned by the folly of their ancestors. They are extremely long-lived; the average Eldar has a natural lifespan of at least a thousand years, and the most powerful of their psykers can survive to be tens of thousands of years old. As a result, most Eldar die in battle while still in their prime, and their population continues to dwindle. So grimdark.
For an Eldar woman to get pregnant once, she needs to have an Eldar male's seed shot several times into her vagina over a fairly long period of time (in other words, the girl needs to have procreative sex several times to make one baby). Due to this, an Eldar can have multiple biological fathers so Eldar family trees tend to be very convulted.
Notable Eldar Gods are Khaine and Isha. The former is in a million pieces at the moment and the latter is held captive by Nurgle. There is also Cegorath, the laughing god, who usually plays paradox poker with Tzeentch, the Deceiver and the Emperor once every week. It's not exactly known how one dimension managed to contain that much dickery in a single location without imploding.
Play Style
As a general rule, the Eldar are an army of specialists. Each unit is engineered for a particular style of fighting but is nigh useless outside of that assigned role. For example, dark reaper squads are known to cripple, if not wipe out completely, entire squads of space marines in a single volley. Conversely, they are incapable of moving and shooting and are comparable to guardsmen in close combat.
Eldar vehicles are known for two things. The first is the fact that they are damn hard to kill. Three out of four damaging hits will, on average, only result in disabling weapons for a turn. The other thing Eldar vehicles are known for is being atrociously expensive for something with so little firepower. Tanks can cost more than 200 pts and are often outgunned by their counterparts at half the price. Unfortunately, since 5th edition is all about the mech, their vehicles are just expensive wrecks.
In summary, an Eldar army functioning as it should is difficult to stop. For this reason, opponents hate them. On the other hand, the army falls apart if given a mean look. For this reason, the owners hate them. They are devastating if they set up, and terrifying if allowed to stick around, but the presence of one Manticore Rocket Launcher or Defiler can collapse an entire Eldar battle line should the space elves not fight with care and foresight.
Eldar as Defenders of the Status Quo
Games Workshop is well-known (read: notorious for) using the Eldar as a gigantic fiat that everything remains exactly as it is (which is to say, in a state of imminent but not quite here yet disaster). In almost every official work that has Eldar in it (such as the Dawn of War series), the Eldar usually provide the "crisis is averted, absolutely nothing else changes" push of the series, causing many players to label them as one of the core reasons Games Workshop has not advanced the 41st millenium's plot in over a decade and a half.
But there are rumblings of great fluff changes in the future from employees who work in GW's fluff department, so it seems that the Eldar are failing at their jobs. HUZZAH!