A letter names the face to turn. No mark means a clockwise quarter-turn, an apostrophe means a counter-clockwise quarter-turn, and 2 means a half-turn. The direction is judged while looking directly at the face being turned.
The six face letters
R is Right, L is Left, U is Up, D is Down, F is Front, and B is Back. The World Cube Association's notation rules define these outer-face moves for NxNxN cubes.
The same suffixes work with U, F, and the other faces. R2 is one half-turn in notation. In Cube Solver's animation, you see the two quarter-turns happen in sequence so the physical motion is easy to copy.
Read a short sequence
R U R′ U′ means: turn Right clockwise, turn Up clockwise, turn Right back counter-clockwise, then turn Up back counter-clockwise. Do one move, check the next letter, and keep the cube's Top and Front orientation in mind. Do not interpret the whole sequence as one simultaneous motion.
Why the arrows help
Letters are compact, but it is easy to reverse a turn when you look at the cube from a different angle. Cube Solver points to the active face and direction on a 3D cube. Its timeline lets you move through steps, and the unfolded map shows the sticker positions before and after a turn.
If you are learning, practice the sequence on the Play screen first. Undo lets you reverse your last manual move without starting over.
Clockwise is from the viewpoint of the face named by the letter, not always from the side of the cube facing you.
See how Cube Solver shows turns.