Mad Cow Disease is actually called Bovine Spongiform Encephalopathy, and it is caused by prions crossing between species, generally by tissue implants, blood transfusion, or blood products such as beef. (Prions are proteins in the body that can cause disease. However, prions do not always cause disease, and they occur naturally in the body, so the immune system doesn't react to them.) Cattle get Mad Cow Disease by eating infected food; however, it doesn't happen immediately. Cattle may eat something that has infected proteins from another animal source and not have Mad Cow Disease develop for months or years. Once the prions infected with Bovine Spongiform Encephalopathy have been passed to a human's body, they cause a variant of Creutzfeldt-Jakob disease to develop (noted as vCJD).
One of the reasons that Mad Cow Disease is so difficult to understand is that prions are not fully understood. They are proteins, which are not alive, so they can't be killed. They can be subjected to conditions (like severe heat) that can render them useless, but this won't work on food because it would destroy the food too. Though they have the potential to become dangerous to the body, prions are not necessarily dangerous (so the body doesn't try to get rid of them). Also, a bad prion can make normal prions become bad as well when it comes into contact with them. Biochemists are attempting to learn more about prions and how they work so that they will in turn know more about Mad Cow Disease.