Halogen light bulbs work by using the same basic principles as an incandescent bulbs. Electricity flows through a set of wires to heat up a tungsten filament. But that is where the similarities end. In a halogen bulb, the filament is encased in a clear quartz capsule in the center of the bulb. This capsule is filled with a halogen gas (hence the name). Halogen gas is also inert and will not react to high temperatures.
As the tungsten is used, it still goes through an evaporation process. But the halogen gas reacts to the evaporated tungsten particles and causes them to stick back together instead of disintegrating and floating free. This causes the tungsten filament to last longer than it would in an incandescent bulb.
Another benefit of using halogen is that the tungsten can run hotter which gives off more light, thus making it brighter than an incandescent bulb. The drawback to this is that it still gives off heat and gets much hotter than regular bulbs. Many house fires have been caused due to this.