A bicycle is a foot move where one foot toe-hooks a hold from above while the other foot pushes against the same hold (or one nearby) from below — the two opposing forces lock the foot pair in place. The position looks like the legs are pedalling a bicycle, hence the name. Bicycles dramatically lock the lower body against the wall, freeing the hands.
Bicycles excel in roofs and steep overhangs where the climber needs to take a hand off but cannot afford to swing out. The opposing pressure of toe-hook plus push creates so much grip that climbers can pause, chalk up, or read the next sequence with both hands free of holds. Some hard boulder problems are unsolvable without bicycling on a key feature.
Like toe hooks, bicycles need aggressive bouldering shoes with full toe rubber. They're extremely calf-intensive — long bicycle holds quickly burn out the front of the lower leg. Practice them on overhanging gym walls with friendly route setters; most modern competition bouldering routes feature at least one bicycle move.