There just aren't enough writeups here...
A bit is also a piece of equipment used with horses. It is basically a what you stick in their mouths and the reins attatch. Horses have a spot in the back of their mouths which, for some strange reason, there are no teeth, although there are teeth in front of and behind this spot. The bit fits right into this spot. The most common material used today is stainless steel. You might also find bits made of copper or rubber. Typically copper is seldom used as it causes excessive salivation, and rubber is used on horses with more sensitive mouths.
The basic purpose of the bit is to serve as a means of communication between horse and rider, although in reality your legs are really the prime means of control in a properly trained horse. The horse is trained to respond to the various forces on the bit, if both sides are pulled back it means halt or slow down. If one side is pulled, it means to turn in that direction. Simple really.
Well, maybe not that simple... There are a lot of types of bits which offer various amounts of control, depending on the horse. The most common type is a snaffle, which is basically two pieces of steel jointed together in the middle so that it is flexible. When the reins are pulled back, the joint flexes and causes pressure to be placed on the roof of the mouth as an extra means of control. The middle piece may also be a straight bar or a straight bar with a raised area in the middle.
Now you've also got to consider the part of the bit that is outside the horses mouth. The most common type used in english riding is an egg butt, which features an egg shaped circle which the reins attatch to. In western bits, as well as some english bits such as a french snaffle, the outside part may have a shank which extends downward that the reins attatch to. This gives leverage which causes the bit to rotate in the horses mouth, brining the middle part up against the roof of the mouth.
On a final note, should you ever find yourself in control of a horse, keep in mind that this is a metal thing in it's mouth. Think how that would make you feel. It should be used as a way of indicating what you want, much like nudging someone to get them to move. You should NEVER jerk on the reins, when I see people do this I want to stick a bit in their mouth and yank it around to show them what it feels like...