This article is from the Feline Leukemia (Cats) FAQ, posted to rec.pets.cats newsgroup. Maintained by Erin Miller with numerous contributions by others.
Retroviruses carry with them an enzyme that causes a process to occur in the DNA known as "reverse transcription." RNA normally pairs up with DNA, copies itself, and thus increases/replicates itself. When an RNA retrovirus does this, it fools the DNA to copy *it*, instead of the normal RNA, thus causing even more of the retrovirus to be created. So as long as a particular cell is affected with the retrovirus, that cell will be affected for its whole life. One would have to kill the cell before it reproduces to eliminate any chance of that cell making any more FeLV or FIV RNA. This is one of the reasons why it is so difficult to get rid of, because you must kill all the cells which contain the virus, and attempting to do this may either kill the animal itself, or it is simply impossible to tell which cells have the virus in the first place. Basically, a retrovirus is a parasite at the genetic level, a DNA-tapeworm, if you will.