RPE stands for rating of perceived effort. It's a method to keep track of how hard the exercise or the workout is in order to avoid over training the body or a muscle. In other words It's a great technique for making sure you don't go over board on your workout and get injured. It's especially helpful for beginners and those people that take weeks off from the gym and are ready to get back in the groove of things.
My best friend once worked out with me (as a training partner) after a long lay off and the next day he could not unbend his elbows. He had to go to the doctors and ended up wearing slings on both his arms for a week. (lol) Now that's over doing it. This could have been avoided if he would have used the Rating of perceived effort method.
Here is how it works: If your new to the gym, aim to start at 70% of effort. The next workout bump it to 80%. The next one after that 90%. You can get creative just don't push at 100% all the time because that's when you risk injury. After each set rate your rating of perceived effort on a scale of 1 to 10.
If you follow this method and fluctuate your percentages in the right way it's a pretty sure way not to get injured.
Another way to work in RPE training is to do it instinctively. Called instinctive training. I only recomend this for people that have many years of experience in the gym and really know their own bodies. It's quite simple; You decide your training intensity based on how strong you feel that day instead of prescribing an intensity days before and trying to reach that intensity when you may not be able to.
If you feel like 70% you push at 70%. If you feel 100% you push 100%. The problem with beginners doing this is that they can't get a sense of what percentage they feel in terms of strength. Many power lifter with years of experience can bench press a measly 45lbs bar and know what type of workout it's going to be and at what percentage they should be pushing.