Simply put: we concentrate a large amount of energy on a very small surface. This operation is performed using a laser beam focused by a lens.
At the point of impact, the material is "vaporized" (you better not be there).
We simultaneously propel an assistance gas to blow away the matter: cutting gas.
We use two different cutting gases:
- Oxygen for steel,
- Nitrogen for stainless steel and aluminium.
The oxygen produces calamine at the cut location on the steels. Calamine is a black residue that remains on the surface of the cut and can be withdrawn with a brush.
Steel can also be cut on demand with nitrogen to prevent calamine formation (eg. for the parts to be painted). It's called the white cut. This generates additional costs though.
There is a comprehensive article about this process on Wikipedia.