"Fury from the sky! Cut them down!" - Thaddeus
Space Marine chapters sometimes need fast-moving, versatile troops that can be easily inserted onto the battlefield and made to quickly close with the enemy. If 8-foot power-armoured posthumans weren't good enough, now they come with jump packs.
Assault Squads are one of the Tactical Squad's cousins. They are of a similar size (5-10), but shun bolters and other long-range weapons in favour of jump packs, chainswords, power weapons, and bolt pistols. Assault Squads are usually deployed from Thunderhawk Gunships, slowing their drop with their jump packs, but it is not unheard of for squads to make use of Drop Pods or even Rhinos. Once on the battlefield they aim to enter close-to-mid-range combat with the enemy, harassing their front lines and using the jump packs to quickly switch targets.
All Codex-compliant space marine chapters move new recruits to Assault Squads after their duty in Devastator squads, using it as a second and final level of upper-division training before the recruit's full induction as a tactical marine within the chapter.
The Blood Angels use Assault Squads as part of their main forces, as opposed to a supporting force. In a departure from the Codex, Blood Angels Scouts who have just received their Black Carapace will be placed in Assault Squads, to allow them a chance to use their natural instincts for close combat without ruining a battle plan by risking a fall to the Red Thirst (Which is bit stupid when you think about it. You'd think they'd put the guys who have proven themselves resistant to the thirst into melee, not the new guys who might wig out at any second. But then again if you're gonna flip your shit and start ripping and tearing, you might as well be equipped to make the most of it, especially since it can actually be useful in that case. And how do you know who's resistant to it unless you put them through the gauntlet of melee.) Every Blood Angel tactical marine maintains his jump pack and close-combat training from his duty in the Assault Squads, allowing the chapter to form massed Deep Strikes of Assault Marines. When not acting as Terminators, the Blood Angels First Company will function as Vanguard Veterans.
Among the Space Wolves, the role of Assault Marine is given to the Blood Claws, neophyte Wolves who are still coming to grips with the inner Wolf and expending their furry by charging the enemy, a lot like their
vampire Blood Angel counterparts. However, they do not use Jump Packs, which are instead given to Skyclaws, who are considered the trouble makers in a Chapter of Space Vikings who don't like flying: "If the Allfather wanted us to fly, he would have given us wings." Which is a pretty retarded statement when you think of it, because if he intended you to shoot xenos filth he would have turned you into obliterators.
At the moment, Assault Marines are kind of shitty compared to bikers because they are so easily killed and lack long range weaponry. If there was an option to give them bolters, or Seraphim-style paired pistols, or chainswords actually did something, or they were a little more affordable they might be worth taking, but at the moment are kinda meh in their current role. They are decent in the Skyhammer Annihilation Force, however, due to their ability to assault after Deep Striking. Additionally, they can use their Jump Packs to both move and assault, increasing their chances of getting into combat immediately.