Wordorigins.org

This term for an important person dates to c. 1731. It’s a reference to the powdered wigs that men wore in the 18th century. Rich and important men would have larger, more expensive wigs. Hence the term.

Contrary to the bit of internet folklore that is floating about, men did not shave their heads under the wigs (or at least most didn’t) and the wigs were not placed in a loaf of bread and baked in order to clean them. That is simply absurd.

(Source: Oxford English Dictionary, 2nd Edition)