Why are lasers more useful for cutting and similar tasks than non-coherent light? 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?
 A: Laser light has an important property: it's initially (in the cavity) very well collimated. If the exit aperture of the cavity is large enough, then the beam remains collimated, which makes it easy to focus it to a very small spot (on the order of wavelength). If the aperture is so small that beam diverges considerably, this means that the aperture has the size on the order of wavelength, which makes the light source basically point-like. Such a beam can be collimated easily, and the resulting collimated beam can be focused* to a spot with size similar to that of the aperture.
An incoherent light source, OTOH, is usually much larger than wavelength of light it emits. The result is that, due to conservation of étendue, such light can't be focused to a spot smaller than the size of the light source, and thus its power density can't compete with that of a laser of similar power output.

*Of course you don't have to first collimate and then focus, this can be done in one step by correct placement of the lens.
A: The acronym LASER is short for "light amplification by stimulated emission of radiation". The stimulation part is important, because this way we are able to obtain high energy densities. In contrast to a light bulb or a LED, the laser beam is also rather directional. This enables us to focus the beam onto "small" spot sizes. Thereby the energy density increases further.
As Jon Custer already pointed out, the coherence is not really that important. A $CO_2$ laser is not particular coherent. However, it efficiently uses the available power and transfers it into the laser modes -- all high power lasers must by multi-mode, because the population inversion factor can't be larger than $1/2$.
