Taps and dies are cutting tools used to create screw threads in metal.
A tap cuts a thread on the inside surface of a hole, creating a female surface which functions like a nut and the die cuts a thread on a preformed cylindrical rod, which creates a male threaded piece which functions like a bolt. The process of cutting the threads in a hole is called "tapping" the hole, so it follows that the process of cutting with a die is called "threading", or sometimes "chasing".
Although there are 3 different types, the most common tap is the taper tap. This tap has a pronounced taper to the cutting edges which gives a very gradual cutting action and is most often used when the material to be tapped is difficult to work, (e.g, alloy steel), or the tap is of a very small diameter and thus prone to breakage.

-Tbone