Laser cutting is a relatively newer technology that uses a concentrated, small laser beam to cut through various materials. The beam is around 0.2mm in diameter. This makes laser a particularly good option if you are looking for accurate cutting on finer designs.
On top of cutting, lasers can also etch or engrave. The difference between etching or engraving and cutting is how far the laser goes. This way, you are able to mark the material by using heat to change the appearance, or to etch away the surface to add a little bit of depth to your design.
The laser machine will read your design file and cut and etch or engrave as required. The main advantage of laser cutting is the low kerf width (the material removed by cutting), but laser is also preferred because of its high precision and high accuracy.