High Intensty Discharge. instead of using a heated wire element that is in a non reactive gas(or a halgoen bulb) HID's pass an eltrical arc through a mix of gasses that "glow" (like xeon, hence some calling them Xeon bulbs) to produce light. however the HID's need a ballast, which takes the 12V of your car, and steps it up as to allow it to arc through the bulb.
the short... HID's produce more light that is also more like day time light( IE not yellow) using less elctricty then a halgoen bulb
of course they are so much brighter they can blind people REALLY baddly at night if aimed wrong.
a rough mesure. a 55W halogen bulb produes ~1000 lumens of light, and a 35W HID kit produces ~3000 lumens of light mmmmmm tasty
a few cars that run these lights OEM, are escaldes, lexuses, and prysus (that i know of, there are more though)
im sure theres better info on wiki, but that should give you enough to know why they are good
-Levi