A 1 to 10 score of how hard a set was, where 10 means no more reps were possible and 8 means two were left in the tank.
The lifting version of the scale, popularised by Mike Tuchscherer, maps directly to reps in reserve: RPE 10 is failure, RPE 9 means one more rep was possible, RPE 8 means two, RPE 7 means three. Below 6 the number stops meaning much for strength work.
Trainers use it because the same prescription adapts to the day. A client who slept four hours still does 3 sets of 5 at RPE 8; the bar is just lighter. On a good day the same set might be 100 kg, on a bad one 92.5 kg, and both were the right session.
It has to be taught. Beginners overrate effort by two or three points, so for the first few weeks ask after each set, "how many more could you have done?", and let the answer set the RPE. Once their guess matches an occasional set taken to failure, the number can be trusted.