Belaying is a way to hold and control a rope for a person who is rock climbing. A climber has to be attached to a rope so they do not fall very far. A person on the ground who is belaying is called a belayer.
The belayer usually puts the rope through a belay device, which lets the rope move through the device in one direction (as the climber being belayed goes up). If the climber falls, the device lets the belayer also hold the rope still, so the climber hangs in the air but does not hit the ground.