Good question, but one for the sake of time, I cannot type out completely here in this forum, besides it'd be VERY tedious. If you're really interested in the "whole story" go to your local library and ask to see Harrison's Principles of Internal Medicine - read ad naseum :-)
Here's the reader's digest version: the virus binds to a specific receptor sites on a specific subset of T cells known as CD4 cells (Helper T's). It is this specific population of T cells that is diminished during the course of AIDS, and since this particular subset of T cells is responsible for directing and controlling most immune functions, you start to see the strange infectious and malignant phenomenon of AIDS. It has been shown that the virus in an effected indivdiual is latent in the exact cells that are deficient during AIDS, and that the body's own immune/response mechanisms to viral infections are alive and working to destroy these same cells when the virus is active.