Halogen bulbs are technically incandescent light bulbs - illumination is produced in both when a tungsten filament is heated sufficiently to emit light or "incandescence." The difference between the two is in the composition of the glass envelope and the gas inside the envelope. A standard incandescent bulb has a heat sensitive glass envelope that contains an inert gas mixture, usually nitrogen-argon. When the tungsten filament is heated it evaporates and deposits metal on the cooler glass envelope (this is why incandescent bulbs appear black at the end of life). This process requires incandescent bulb filaments to be heated less than optimally to give the bulb a reasonable life. The lower filament temperature gives incandescent bulbs their typical orange-yellow, warm appearing light.
Halogen light bulbs utilize a fused quartz envelope ("capsule") allowing for higher temperatures. Inside the quartz envelope is a vapor, originally iodine, now usually bromine. The tungsten filament evaporates as usual but the higher temperatures are sufficient to cause the tungsten to mix with the vapor instead of depositing on the envelope. Some of the evaporated tungsten is re-deposited on the filament. The combination of this regenerative cycle and higher filament temperature results in a bulb that has a longer life and slightly higher efficiency than standard incandescent bulbs. The higher temperature filament also produces the "white" light often associated with halogen bulbs.
Halogen is the name given to a family of electronegative elements, including bromine, chlorine, fluorine and iodine. Halogen bulbs are referred to variously as "tungsten halogen,""quartz halogen" or simply "halogen." The term "J" bulb (some manufacturers use the letter "J" in their halogen bulb designations) probably comes from the German word "Jod" which in English is "iodine," one of the elements in the halogen family.