Definition
A set or a block in which the lifter does as many reps, or as many rounds, as possible at the given weight or in the given time.
Two uses. A rep AMRAP is one set at a fixed weight taken to technical failure, like the "5+" last set in 5/3/1: it tests progress and calibrates the client's RPE. A rounds AMRAP is a conditioning block, twelve minutes of a circuit, score in rounds.
Rules: stop at technical failure, keep at least one rep in reserve on heavy barbell lifts, and cap the reps (stop at 15) so a light day does not turn into junk volume. One AMRAP per session is plenty.
The rep count is the progression. Same weight, more reps next month, is the whole point.