It stands for Royal Conservatory of Music. It is a Canadian music education system, (for not only instruments, but also speech giving) containing 12 levels--and introductory level, ten grades, and ARCT (Associate of the Royal Conservatory of Toronto). At the ARCT level you can have a performance ARCT, a teacher's ARCT, a Theory ARCT, or a Compostion ARCT. (There might be others, but not that I can think of). Basically, you decide what direction you want to go after you complete the grade ten exam. Some do none, some do more than one. It depends what you want to specialize in.
Each grade has repertoire from different periods, technical exercises and studies, sight reading, sight clapping, ear tests, and theory.
Exams are not manditory, except for grade ten, if you want to get an ARCT.
It's similar to ABRSM. I think a branch of RCM has started in the U.S. now too.