Laser cutting uses a continuous or pulsing laser beam to cut. The beam contains a lot of energy which is concentrated at one point. When the beam hits a material, the material vaporises, burns, melts or cracks. Exactly what happens depends on the material and the laser cutting machine.
Laser cutting results in fine tolerances, because the laser beam is thin and also because it is possible to aim very accurately where the cut is wanted. Since the laser beam is so thin, materials are not particularly affected by thermal heating. The thin beam also makes it possible to cut complex shapes in very thin materials.
Some laser cutting machines also have a third axis, sometimes referred to as a z-axis, which makes it possible to cut three-dimensional.