A collet is a holding device that forms a collar around the object to be held and exerts a strong clamping force on the object when it is tightened. It may be used to hold a workpiece or a tool.
Collets generally have a narrow clamping range which means a large number are required to hold a given range of materials, unlike a chuck that will generally cover the full range that the machine is designed for. The collet's advantage over the chuck is that it offers much higher precision when reclamping a single object to work it in a series of steps.

Woodwork

On a wood router (a hand-held or table-mounted power tool used in woodworking), the collet is what holds the bit in place. In the U.S. it is generally for 1/4 or 1/2 inch bits, while in Europe bits are most commonly 6 mm or 8 mm. The collet is hexagonal on the outside so it can be tightened or loosened with a standard wrench, and has threads on the inside.

Metalwork

The two top left collets are the side and end view of one style of collet, the two right collets are from a smaller range.
The lower image is of a dissassembled pin chuck that is used to hold small drills or work pieces. The left most part is the body, the collet is shown protruding from the body and the nose cap is seperate, on the right.
In use, the part to be held is

• inserted into the collet
• the collet is pushed fully into the body ( which has a taper to match the collet machined into the front)
• the nose cap is screwed onto the body ( which also has a matching taper machined into it)

when the nose cap is tightened properly, enough force is applied to the collet that the taper at the front and back of the collet are pushed into their matching tapers, causing the collet to constrict in diameter. This constriction exerts considerable force onto the shank of the workpiece (drill) that is being held in the collet. It is then securely held against any forces it may encounter during normal operation.