According to Wikipedia:
Astral projection (or astral travel) is an interpretation of out-of-body experience (OBE) that assumes the existence of an “astral body” separate from the physical body and capable of travelling outside it. Astral projection or travel denotes the astral body leaving the physical body to travel in an astral plane. The idea of astral travel is rooted in common worldwide religious accounts of theafterlife in which the consciousness’ or soul’s journey or “ascent” is described in such terms as “an… out-of body experience, wherein the spiritual traveller leaves the physical body and travels in his/her subtle body (or dreambody or astral body) into ‘higher’ realms.” It is frequently reported in association with dreams, and forms of meditation.
Patients have reported feelings similar to the descriptions of astral projection induced through various hallucinogenic andhypnotic (including self-hypnotic) means. There is no scientific evidence that there is any measurable manifestation of a consciousness or soul which is separate from neural activity, and there is no scientific evidence for the contention that one can consciously leave the body and make observations. Attempts toverify that such has occurred have consistently failed in spite of the variety of pseudoscientific claims to the contrary.
To learn how to astral project/have an out-of-body-experience, this article by The Mind Unleashed, has some great tools to learn how to travel the astral world: “10 Effective Techniques for experiencing an OBE”.