A drill chuck is a specialized clamp designed to hold drill bits in place while they are being rotated by the drill. The chucks nearly always have three jaws that press down on the drill bit so that it won't slip when it pressed against a surface that it needs to penetrate. They can also be used to hold bits and tools heads of other rotary tools.
Once a bit is inserted into the chuck, the jaws are tightened on the bit by rotating a threaded screw. The screw threads and the threads on the backs of the jaw pieces are on an angled surface. By turning the screw to the right, the screw moves down the tapered surface to the thicker area, which causes the jaws to press against the bit.
Hand-tightening the chuck is easy. You simply twist the internal screw to the right as tightly as you can, but the chuck can loosen if there is too much torque applied to the bit when drilling. That's where a chuck key helps. The end of the chuck key inserts into a hole on the side of the chuck so that a gear ring on top of the internal screw and a small gear ring on the chuck key interlock. By turning the chuck key, you get greater torque on the internal screw to tighten it even better than by using your hand alone.
To remove a drill bit, the internal screw is turned to the left, either by hand or using the chuck key. The screw moves up the tapered surface to the thinner areas, which loosens the jaws so the bit can be removed.
High-precision drills may use ball thrust bearings to reduce friction in the chuck and maximize the torque. Hammer drills use a special direct system that hold the bit in place with wedges moving into a groove in the bit.