This question gets asked every year, and we usually answer with this quote from the N.Y. Times.

East Third Street becomes Great Jones Street between Broadway and the Bowery. Who was Jones and what was so great about him?

Jones is Samuel Jones, a lawyer sometimes called Father of the New York Bar. He owned the land on which Great Jones Street now runs and bequeathed the property to the city with the caveat that any street that ran through the land be named for him.

In 1789 a street was opened there, but New York already had a Jones Street in Greenwich Village. So the new street was named Great Jones Street because it was wider than the norm.

In his desire to be remembered, Jones may have linked himself with a different aspect of the city's culture. The slang term "jones," meaning an addiction to drugs, is said to have originated among addicts who lived in Great Jones Alley, off Great Jones Street, between Broadway and Lafayette Street.