Rendering, in Reaper, is mixing down to a chosen format.
You set up a mix & select render then where & under what name you want the files saved the bango you have a .wav or .MP3 file of the mix or current set up of track.
Funny appellation I agree.
It's from the video NLE world and before that from drawing/painting. A nonlinear editor would draw each frame of the finished video based on the original material and the processing applied. NLEs and DAWs overlap and so the term got adopted by many DAWs, especially the ones with video editing capability like Sony Vegas.