This is an acronym for 'As many rounds/reps as possible' - This will come with a specified time. For example, a 60 second AMRAP of push ups would require you to complete as many push ups as you can in 60 seconds.
The term 'AMRAP' is often followed by a number. This number is the amount of time you have to complete the metcon.
You will need to manage your effort during an AMRAP. You should finish feeling like you don't have any more reps in you. On the other hand, beware that if you start off all guns blazing, you may burn out too fast!
In the likely event that you need to catch your breath, take 3 or 5 deep breaths before resuming. On shorter AMRAP's (10 minutes or less), Drink water BEFORE or AFTER you start so that you aren't wasting time.
Consider that the clock is ticking DOWN, so move as fast as you can. The clock starts as soon as the first rep is initiated, and stops as soon as the timer hits the specified time of the AMRAP.
Here is an example of a 40 second AMRAP (this is incredibly short as an example), with one round consisting of:
5 x burpees
5 x squats
Over the course of the 40 seconds, 2 rounds are completed.
Even if you know you wont have time to complete an additional round - go for it anyway to get the full benefit and increase your results.