It's easy to compare the asura to the commonplace fantasy archetype of the gnome: among the playable races, they're the smallest in stature, rarely cresting the four-foot mark, and also the most technologically-minded, using their knowledge of both magic and materials to craft fearsome golems to protect their home city of Rata Sum. Rata Sum is not technically their "home city," though. The asura originally dwelt far underneath the surface of Tyria, but were driven from their underground empire by a terrible monster known as the Great Destroyer over two centuries before the events of Guild Wars 2. Cut off from their ancestral home, the asura took to the surface of Tyria and, stumbling across long-abandoned ruins of a presumably long-dead race, decided to claim them for their own and rebuild them. Thus was borne the floating, geometric city of Rata Sum and its uneasy balance between the ancient world and the current one. While they're not necessarily religious, the asura do adhere to a belief in the Eternal Alchemy, which strives to discover the greater purpose behind the struggles of Tyria.
As mentioned, many asura are artificers, with the art of "golemancy," the crafting of golems, being an especially revered one among the people. They're not limited to merely creating magical creatures, though: the asura also created the asura gates that link together the capital cities of all of the races (through which you'll often find yourself traveling, especially after you conquer your race's starting zone). You'll be able to align your character with a specific asuran College during character creation, to further enhance your personal story and role-playing opportunities. The College of Dynamics is the most impulsive of the group, preferring to forge ahead with an experiment rather than work on theory. They can be contrasted with the College of Statics, possessed of more reserved and withdrawn students, who focus on projects with a more grand sweep to them, such as ensuring that Rata Sum continues levitating. Lastly, the College of Synergetics focuses on a more philosophical view, looking for common threads in the Eternal Alchemy and researching the link between mind and machine.
In addition to these colleges, your asuran character will quickly come across the Inquest, an asuran corporation that pushes the boundaries of asuran ethics in their technology "innovations," such as by enslaving members of sentient races inside the bodies of golems. They function within asuran society, but are widely distrusted by non-members, perhaps for good reason...
The asura have three Utility skills: Pain Inverter, which places the confusion condition on nearby enemies while allowing the caster to reflect a portion of incoming damage; Radiation Field, which causes poison and weakness on enemies in an AOE; and Technobabble, which causes the target to be dazed. Technobabble may be the most generally useful of these skills, as it'll allow you to interrupt spellcasting regardless of your weapon.
The Elite racial skills available to the asura are, unsurprisingly, related to golemancy. When you reach level 30, you'll be able to unlock Summon 7-Series Golem, which will, as the name implies, summon a golem that will fight alongside you for 40 seconds. If you're in the mood for something more hands-on, you can also unlock Summon Power Suit, which enables you or an ally to hop into a mechanized fighting suit and unload on your enemies using its special skills. The most expensive Elite skill available to you, however, is Summon D-Series Golem, which will bring down a much more powerful golem to aid you in combat.