A summary of why collets are needed and the parts involved.
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Where does it sit?
A collet (C) is used in a spindle motor (D), to clamp a cutting tool (A) to the end of the spindle taper (E). A nut (B) is used to compress the collet which applies a clamping force to the tool.
A: Tool
B: Spindle nut
C: Collet
D: Spindle unit
E: Spindle taper

What the collet needs to do
Provide the maximum amount of clamping force
By clamping force, we mean the amount of grip the collet has on the tool. A high clamp force:
Provide the minimum run-out
By run-out, we mean the distance the tool mis-aligned from the center or rotation (shown below in red).

A low run-out value means:
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