This article is from the Feline Leukemia (Cats) FAQ, posted to rec.pets.cats newsgroup. Maintained by Erin Miller with numerous contributions by others.
In sum, once the virus gains entry (usually via saliva or mucus membranes) it will reproduce in the lymph tissue which is your cat's first system of immune defense. Some cats are able to mount a successful immune response against it and defeat the virus at this stage. In cats who don't successfully destroy the virus here, the virus will then move into the bone marrow where red and white blood cells are produced. It may stay latent in the marrow for many years. After that it will attack other tissues, including possibly causing a breakdown in several stages of the immune response system.