Haha, I was hoping tracie would reply, because she seems to be the expert on it and is doing lots of research on the topic and stuff. But seeing as she hasn't seen this thread, I'll do my best to tell you what I know, though some of it might be wrong/outdated.
Basically it's a virus that can do lots of things to them. Some dragons manage to carry it in their systems with no ill effects, some suffer weakened immune systems making them more susceptible to parasites and opportunistic infections, some just don't gain weight properly and generally fail to thrive, some have liver damage, and in some (from what I've read mostly very young babies) the infection will travel to the spinal cord causing neurological symptoms like stargazing, twitching, seizures, and eventually death. There is no treatment or cure for the virus, symptoms of other infections are managed as they crop up, but I think I read somewhere that dragons with adenovirus are more susceptible to nasty side effects from other meds.
There is much debate about what proportion of dragons are infected but symptomless, and when a dragon is found to have it on necropsy, there is debate about whether it was the virus that killed them or an opportunistic infection allowed to thrive due to the presence of the virus, or whether something else lowered their immune systems allowing them to catch the virus and another infection at the same time.
It is also relatively hard to test for as the dragon may carry the virus but if the virus isn't shedding at the time, a test may come back clear. I think the general thinking now is that if a dragon has 3 negative tests (and hasn't been exposed to other dragons in the meantime), it's a good bet that it isn't carrying the virus.
If you want more correct and up to date info, your best bet is to PM tracie as she is the resident expert on this disease (and most other beardie related things!)