The list of played moves in endgame problems serves several purposes. It allows you to see the path you have followed while the problem is active, but it also provides extra details on the moves you played after the problem is finished. You can also play through different lines after the problem is over, and see the variations added to the move list.

The annotations on the move list after the problem is over show moves that were not the best move in the position. For example M10(M8) shows you played a move that was mate in 10 where the best move was mate in 8. L10(M2) shows that you played a move that leads you to lose (i.e. be mated) in 10 moves, where the best move would have had you mate your opponent in 2 moves. D(M3) indicates a move that draws when you could have mated in 3. You can hover your mouse pointer over the other moves to find out how many moves they are away from mate.