Undo steps back up to 100 moves, restoring the board and score each time. Your personal best score is kept even if you undo.
Undo takes back your last move, and you can keep pressing it for up to 100 moves. Each undo puts the tiles and the score back as they were before that move.
What undo does not do
An undone move does not replay the same random tile. If you play the move again, the new tile may appear somewhere different (which tile appears after each move).
Saved progress
Your board, score and undo history are saved in this browser, so a reload or a closed tab does not lose them. Your personal best is not lowered by undoing. Undo is there to recover from a slip, not to replace a plan: the 2048 strategy guide shows how to avoid the slips, and the full rules cover the rest.