This stands for “as many rounds (or reps) as possible.” Usually it will be with in a given time frame. If a time frame is not given, it is in one continuous, unbroken set. For example:
20 minute AMRAP
-5 pull ups
-10 push ups
Each time through that sequence of exercises is one round. Complete as many rounds in 20 minutes as you can. Or, AMRAP push ups would be the number of push ups you could complete in one set without resting.