Incandescent
Incandescent light bulbs work by passing electricity through a thin wire (filament) made of tungsten which then heats up and gives off light. To prevent the filament from oxidizing or evaporating, it is enclosed in an airtight bulb that either has a vacuum or is filled with a chemically inactive (inert) gas like krypton, argon, or xenon. Most the power delivered to the bulb is converted to heat or to invisible light like infrared, but visible light is also produced.
Because the power is applied directly to the bulb, bulbs are designed for certain voltages, for instance 3 volts. A common type of flashlight bulb is a flanged PR bulb used in Maglite C and D cell flashlights. Some lights require bulbs that are threaded. Smaller bulbs, like the the xenon light included in the Mini Maglite are "bi pin" and have two pins that fit into sockets.
To achieve the maximum brightness from an incandescent bulb, more power is applied, but this greatly decreases the overall life of the bulb. Under-driven bulbs will last for a long time but produce much less light.
While incandescent lights may last only a few hundred hours and aren't very efficient, the advantage is the bulbs are generally pretty inexpensive, don't require any supporting electronics or drivers, and give a white light with a broad spectrum and a high color rendering index (CRI).
Halogen lights
There is a family of elements called halogens that includes chlorine, iodine, and bromine. By adding some of these gases inside a bulb, a process sets up where tungsten evaporating off of the filament is replaced. This allows the filament to be driven harder and achieve longer life than would be possible without the presence of the halogen and also increases efficiency of the bulb. However halogen lights operate at extremely high temperatures.