RMS is short for Richard M. Stallman. Sometimes also expanded as RavingMadSocialist.
Look at my HackersBeard, everyone! -- RMS
Richard Stallman wrote Emacs, gcc(1), make(1); all sorts of the useful stuff on a Linux system. He did this as part of the GNU (GNU's Not Unix) project, to try and replace the commercial Unix with a Free OperatingSystem.