Halogen headlights use a sealed bulb with a filament made of the element tungsten and contains an inert gas and a small amount of an element from the halogen series in the periodic table.  Iodine and Bromide are commonly used halogens in these light bulbs.
A chemical reaction called the halogen cycle is caused when the halogen gas and tungsten are combined.  This reaction allows for a very high operating temperature which gives these types of bulbs a long lifespan and allows a high color temperature light to be achieved.
For automotive use, halogen headlights are most commonly available in 6V, 12V and 24V – with 12V being the most common as that is standard voltage of your cars electrical system.
Bulbs can be either a single or double filament.  With single filament bulbs you will often have a distinct bulb for each of your high and low beams.  Single filament bulbs often have a wattage range between 55-100W.   The double filament halogen headlight bulb allows a single bulb to operate both the high and low beam functionality in one bulb.  This is accomplished by each filament having different wattage capabilities.  The low beam will operate between 55-100W and the highs between 60-130W.
There are several standard connector types used to connect the bulb into the electrical system of your car.

Single Filament

• H1 axial filament
• H2 axial filament
• H3 transverse filament with heat-resistant cable

Double Filament

• H4 dual filament bulb
• H5 similar to H4, bigger connection adapter
• H7 dual filament bulb

H4, H5 and H7 bulbs are probably the most common bulbs used in today’s halogen headlights.
A handy trick that I learned with H4 bulbs:  often manufacturers will have a small metal clip that connects the actual bulb connector to the wiring harness.  It took two parts specialists and myself to figure this detail out.