A bit (router bit, end-mill, milling bit) is a round cutting tool with at least one sharp, cutting edge that is used to remove material from a piece of stock. To be used, the bit is spun at high speed in a router or spindle and gently pressed into the material to be cut. The cutting edge of the bit digs into the material and peels off a small piece of waste--called a "chip". Most bits are designed to clear this chip up and away from the cutting line (know as the kerf) to make room for further material to be removed.
While most router bits will have just a single cutting edge (known as "single flute" or "O-flute" in the case of some special bits) more sophisticated bits (more often called end mills) will have multiple flutes. The number of flutes is part of what determines the rate at which the bit can be driven through the material and the quality of the cut that it leaves behind. A multi-flute bit will typically produce a higher quality (smoother) finish on the faces that it cuts. However--because routers spin at such high speeds--multi-flute bits can become very hot during operation and may burn the material (in wood) or melt the material (in plastic and soft metals) causing the bit to break and the cut to be ruined.
Choosing the right bit for the application is vital to the success of a project. Because bits tend to cost around $30 each--broken bits can add up quickly and become a major source of frustration in an operation.