I'm working a lot with lasers the last few years, and trying to understand the basics. So some of what I say next may be wrong or partially correct - if I find that out, that will be valuable.
As I understand it, a laser is a light source (these days it might well be a diode) where the frequency and phase of the light is coherent. If you use suitable optics, you can then make a parallel beam which can then be focused onto a spot. If the spot is small enough and the power high enough, that beam can then be used for applications such as cutting, basically because it heats the surface it falls on to very high temperatures.
My question is this : couldn't you do the same thing with (for instance) a high power LED? You can certainly have a fairly narrow band of frequencies from a non-laser, if that makes optics design easier. So why, then, do we favour lasers for this kind of application? Why do we prefer the light to also be phase-coherent?