Definition: A very important person
Example: Mr. Peabody was a big wig in town. After all, he owned most of it.
Its not a great stretch of the imagination to figure out how the phrase ‘big wig‘ came to be.
It owes a lot to the Sun King himself, Louis XIII. Louis was bald, or ‘follicly challenged’ as he preferred his condition to be described. So, he took to wearing wigs. His group of hangers-on in the court of Versailles took to wearing them as well. Then, the rest of the French aristocracy. Then the the rest of the upper echelon of Europe followed suit. And then the competition began. The bigger, the more extravagant the wig, the better. Decoration was widely encouraged.
Obviously, the buying and maintenance of such extraordinary constructions were an expensive business. Only the wealthiest, most influential people could afford them. As a rule of thumb; the bigger the wig, the more important the person.
On a little side note, before these piles of hairs became known as ‘wigs’, they were known by the more flowery term ‘periwigs’. Iddy thinks the world is a slightly sadder place with the shortening of the term.