The formal definition for Available is given in TFA.
You're correct that the theorem doesn't address latency requirements. There are all kinds of things it doesn't address. The point of it is simply as you say - you must give up consistency to have availability in the face of a partition, or vice-versa. Some vendors of distributed systems would have us believe otherwise. This theorem gives us a framework to understand at a very basic level the trade-offs that must be made in distributed system implementations. That isn't really very much for as much airtime as it got, which I suspect is what your contention is with.