RPE stands for "rating of perceived exertion". In strength training the scale describes how hard a set was and is tied to reps in reserve (RIR): RPE = 10 minus RIR.
The original RPE scale comes from endurance sport and asks about your general sense of effort. For lifting that is too vague, because a long set can feel awful even with several reps left. Zourdos et al. 2016 therefore described a scale linked to reps in reserve.
The levels
RPE 10 means no further rep was possible. RPE 9 means one more would have gone, RPE 8 two, RPE 7 three. Half steps such as 8.5 mean one for sure, maybe two. Below RPE 7, estimates get unreliable. For muscle growth, most working sets sit at RPE 7 to 9.
Planning loads with RPE
Every combination of reps and RPE corresponds roughly to a percentage of your 1RM. A widely used chart comes from Mike Tuchscherer.
Example: 100 kg for 5 reps at RPE 8 equals 81.1 percent of 1RM according to the chart. Your estimated 1RM is then 100 ÷ 0.811 = about 123.3 kg. For 3 reps at RPE 9 (89.2 percent) you get about 110 kg. This is a worked example.
The real advantage is called autoregulation: a plan that says "5 reps at RPE 8" adjusts the load to how you feel that day. During a cut, RPE also works as an early warning. If it climbs clearly over several weeks at the same load, you are losing performance, and your deficit may be too large.