Sometimes top roping is impossible because the climb is longer than one-half a rope length or because the climbers don't have access to the top of the cliff to fix the webbing. The rope is clipped into the protection. The second climber belays the lead climber. Biomechanics are crucial to climbing. Hand jams allow climbers to grab holds in seemingly impossible places.
Climbers also manipulate their center of mass by working their bodies away from the rock face.
This puts more force onto their feet. High-tech climbing shoes make good use of that force. Climbing techniques put a variety of forces to work. By keeping their weight balanced over their feet, the climbers remain stable. Their outward push forces their shoes into the walls and the shoes generate an upward frictional force which opposes gravity and allows the climbers to ascend.