Why isn't normal light used to cut stuff? Like many people, I have tried burning stuff with magnifying glass. Where I live, the power of sun is some 600 watts per square meter at most. If my magnifying glass is 10cm in diameter I have only 4,7 watts on my focus point. It can light paper instantly.
This makes me wonder why do we have laser cutters. A few hundred watts of ordinary light could do the same. It would seem much easier to have just ordinary light source. No expensive CO2 or fiber lasers. Just a simple high power led for example.
I guess that the reason is that laser light is coherent. Another thing that comes to my mind is that sunligt is practically collimated as the sun is so far. Maybe achieving same with artificial light is not so easy.
What is the real reason?
 A: This has nothing to do with coherence or the fundamental physics distinction between "normal" and laser light.
It's simply a question of finding a source that is intense enough to induce a fine cutting edge. That is, the source must be both powerful and one must be able to concentrate it into a very small spot. Cutting happens when there is highly intense local heating in a very small area of the sample.
The mechanism of stimulated emission allows the generation of huge amounts of light all in exactly the same momentum state. What this means is that the output is high power and very nearly a plane wave, with a low aberration wavefront. Such a wave can be focussed to near to a diffraction limited spot. Thus stimulated emission enables both the fundamental requirements of power and low wavefront aberration, equating in this case to high ability for concentration.
At $10{\rm \mu m}$ wavelength, that of a ${\rm CO}_2$ industrial machining laser, that implies a spot size of about $20{\rm \mu m}$ focused through a $0.3NA$ optical system. With thousands of watts continuously output, this equates to an intensity of terawatts per square meter at the "cutting edge".
In contrast, the Sun is not a collimated source - it is an extended one. The best you can do is focus it down to a tiny image of the Sun. Let's do our calculation for a 0.3NA lens one meter across. The distance to the sample is then about 3 meters. The image of the Sun is then $\frac{3}{1.5\times10^{11}} \times 5\times 10^8$ meters across, or about one centimeter across. Through our one meter lens, we get about $600{\rm W}$. So we get about the same power as in our laser example (somewhat less) through an area that is $\left(\frac{0.01}{2\times 10^{-5}}\right)^2 =2.5\times 10^5$ times as large. Our intensity is thus five or six orders of magnitude less than in the laser example. 
There is limited ability to improve this situation with a bigger lens; as the lens gets wider, you need to set it back further from the target, with the result that the area of the Sun image grows at the same rate as the area of the lens, and thus the input power. The intensity stays roughly the same.
LEDs
The OP also asks about LEDs. Although modern LEDs can output amazing powers, they, like the Sun, are also an extended source, comprising a significant area of highly divergent point sources, so the light output has a high étendue and cannot be concentrated into a tight spot. This highest power  LEDs needfully have a large area semiconductor chip whence the emission comes. In a laser cavity, it is also true that the first seem emissions are also highly divergent, and the first pass through the gain medium produces an amplified spherical wavefront. However, the design of the resonant cavity means that only a small, on-axis section of that spherical wave bounces back into the cavity, most of it is lost. On the second pass, we have an amplified, lower curvature wavefront; most of this is lost at the other end of the cavity too. During the first few passes, therefore, the process is quite inefficient, but on each bounce the wavefront gets flatter and flatter as only light components directed accurately along the cavity axis can stay in the cavity and the efficiency of recirculation swiftly increase. Through this mechanism of resonance, therefore, the stimulated emission process is restricted to only the most on-axis components of the light. Thus, the combined mechanisms of resonance and stimulated emission co-ordinate the whole wave so that ultimately it is a plane wave, propagating back and forth in a cavity, spread over a relatively wide cross section so that heat loading from any losses are not damaging to the cavity. This near-zero étendue, low aberration field is easily focused to a diffraction limited spot.
Solar Furnace
User Martin Beckett gives the example of the Odeillo solar furnace:

You can however use lots of lenses (or mirrors)

This is in keeping with my solar lens example above. A solar furnace is great for furnace applications, such as mass energy production or smelting. But the focused light lacks the intensity needed for cutting. The intensity in this example is about the same as for our one meter mirror. The furnace focuses several megawatts through a 40cm diameter focus, and a a few megawatts through a 40cm focus is about the same intensity as one kilowatt through a 1cm wide focus, which is what we had for our solar lens example.
A: In theory, sunlight can be used to cut things. In the paper Concentration of sunlight to solar-surface levels using non-imaging optics, Gleckman et al demonstrate the ability to concentrate the radiant flux of sunlight by 56,000 times, getting to within one order of magnitude of D. Rodriguez's answer for laser light flux above.
However, conservation of etendue means that the maximum amplification is inversely correlated with the acceptance angle, meaning that the sun tracking required to keep the concentrated point at the highest temperature would need to be extremely precise, and probably several times more expensive than a CO₂ laser, solar generator, and battery. Add to this the fact that the solar concentrator setup can't "store" sunlight when it's not in use (which means that every minute that it has suitable sunlight and isn't in use is a minute wasted) and it becomes even more uneconomical.
A: I only looked at the other answers quickly, but I haven't seen anyone mention the role of material properties. 
IIRC, many materials absorb very well at 10.2 um. If they didn't, it wouldn't matter how much power you put on it because it'd all be reflected (a potential safety or equipment damage hazard).
Since you have good absorption and readily available high power sources, you can create very hot localized spots on a material as the others mentioned. These steep temperature gradients enable you to make clean cuts. 
A: Because the energy contained in sunlight is not high enough to increase the rate of vibration of the atoms of an object to the point where the bonds break. The melting and boiling points of the compounds constituting an object are what determine the nature of light that can be used. Lenses can be used to reduce the wavelength of light hence increase it's vibration but with sunlight, numerous changes have to be done such as using a solar panel and then later transforming the resultant electric energy to laser or to power a cutting tool (in essence sunlight is being used)
