Best: Exactly what it sounds like.
Great (!): The only good/reasonable move in any given position. Note that the move in question must actually be good. If all of your legal moves suck (zugzwang), but one in particular sucks less, it probably won't get a "great" rating.
Brilliant (!!): A move that sacrifices a piece or ignores a threat on one; however, no matter what your opponent does, it's their position that will worsen.
Best, great and brilliant are all best moves, but best is just BEST, and great is when there is the only move that works, and a brilliant is something like a good sacrifice