Astral projection is a practice which involves trancework, or altered states of consciousness. Basically, a person who APs will go into a deep meditative state, and (feel like they) separate from their body. Their perception in that state is not of their immediate surroundings, but of things 'other' than what is physical reality. Some will say they travel to other plains of existence, specific non-physical locations and realms, dream worlds, and so-forth.
Although it is a fairly common practice, no two people experience exactly the same thing, and it is all a belief, and not something provable with fact.