What do viruses do during incubation period?
during the incubation period the virus is typically increasing in numbers and spreading between cells. It takes a while for symptoms to become obvious because it takes time for enough damage to be built up in the tissue to become noticeable.
Take for instance the Rhinovirus which causes the common cold, once you become infected it is a day or so before enough damage has been caused to the tissue at at the back of the throat to give you a cough.

In addition some of the symptoms of infection are caused by your own immune system as a way of fighting the infection. For instance inflammation is often a sign of infection but is typically caused by the immune system to allow the movement of plasma and leukocytes into the infected tissue. As the immune system requires time to recognise and respond to a pathogen this leads to the delayed onset in symptoms.

AIDS is actually a syndrome caused by the HIV virus. the HIV lifecycle occurs CD4+ T-Cells, after infection occurs the immune system tries to cope by destroying the infected cells but over long time the infected population increases. The immune system becomes more and more compromised until the CD4+ cell count drops to a level where the patient is diagnosed with AIDS. At this point the immune system is compromised and the chance of a secondary infection by a different organism increases which the patient can no longer fight off. The actual cause of death for someone infected with HIV is rarely the HIV itself but is quite often a different agent.