The short version is that corals are photosynthetic. They get much of their food and energy from the sun. So you need to have a light that can replicate the sun over your aquarium. The two important things to look at are the intensity of the light and the spectrum. Lights that will support corals are very bright. A ‘regular‘ LED aquarium light might be 8 or 10 watts, whereas lights designed for corals are often 100 or 150 watts or even more. The color of the light, or the spectrum is important as well. Corals need light of a certain wavelength to be able to use it. If you just got the brightest light that you could find and put it over your tank it still wouldn’t support corals unless it had the spectrum that the corals needed.
There are a lot of options for lights that will support corals, but none of them are practically