High-intensity discharge light bulbs are completely different than a halogens. Halogen bulbs use a filament, where current is passed through and subsequently causes the filament to glow with such intensity that it produces bright light. HID bulbs are a filament-less design.
They work similarly to fluorescent lighting, but are much brighter and a lot more efficient. They two electrodes inside, and they're filled with a combination of gases (xenon is a common one) and metallic salts. When electricity passes through the bulb, an arc is created between the 2 electrodes.
This arc excites the gas inside the bulb (via heat) which in turn vaporizes the metallic salts (sounds like Star Wars, doesn’t it!). These vaporized salts then sustain the arc and become the root light source. HIDs require a high initial electrical input to started, but once the salts begin arcing, the input is significantly reduced, resulting in their overall efficiency.
This entire process is actually more efficient than a regular halogen bulb and produces more light per unit of electricity input! Halogen bulbs typically run on a 55W pull whereas HIDs use 35W. HIDs characteristically produce 2-3 times the lighting power as halogens.
HIDs provide a clearer light beam that extends both wider and farther than a conventional halogen bulb. Because halogen bulbs produce less light, what light there is needs to be concentrated and aimed to priority locations, such as right in front of you.
This priority aiming leaves less light to illuminate the sides of the road and results in lessened peripheral visibility. HIDs have more light to use, so it can be spread evenly and everywhere from your headlights across the road.