Asgard is the world that is inhabited by the Aesir gods. After the Aesir-Vanir war, some of the Vanir have moved to this world to live among their former enemies.
There are multiple halls in Asgard, each of which had its own purpose and belonged to a specific god or goddess. The most famous hall was Valhalla, where Odin feasts with his Valkyries and half of those that died an honorable death in battle to await the events of Ragnarok. The other half of the slain reside in Fólkvangr with his wife, Frigg, who had a hall of her own. Then there are Breidablik, the most beautiful hall that belongs to (the himself beautiful god) Baldr, and Himinbjörg, the fortress from which Heimdall protects the Bifröst. Thor had his own hall, Thrudheim, where he lived together with Sif and their offspring.
Asgard is protected by walls that have been built by a rock giant (for free in fact, as Loki tricked him into doing so). After that point, it could supposedly only be accessed through the Bifröst.