Each letter is one side of the cube, as you hold it right now: Up (top), Down (bottom), Right, Left, Front (facing you) and Back. A letter alone means: turn that side a quarter turn clockwise, as if you were looking straight at that side. An apostrophe (U', say "U prime") means anticlockwise, and a 2 (U2) means a half turn.
The app names moves from your side of the cube, so R is always the layer on your right, whichever colour that is. Turn the whole cube and the names of the moves still to do update.
Click a move to see it.