A mantle (sometimes "mantleshelf") is a move that ends with the climber pressing themselves up and over a horizontal feature — pushing down on the hold rather than pulling. The motion is identical to climbing out of a swimming pool: arms transition from pulling overhead to pushing down beside the hips, and the climber uses tricep and shoulder strength to lift their body over the lip.
Mantles appear at the top of boulder problems, when topping out on slabs, and any time a climber needs to transition from a hand-hold to a foot-hold (the same hold). The hard part is the hand transition — keeping balance while one hand pushes down and the other moves up to a higher hold or onto the ledge.
Good mantling uses the legs heavily. Once the elbow rotates from up-and-pulling to down-and-pushing, the climber should drive with the leg they've flagged or stepped onto, taking weight off the arms as soon as possible. Indoor gym route-setters often build deliberate mantle finishes to test this skill.