How'd Jack-o-Lanterns get their name?

From FUN TRIVIA.com:

Jack O'Lanterns have been part of Halloween for hundreds of years in both the U.S. and Great Britain, where our familiar 'pumpkin lanterns' are often made from large turnips. The name 'Jack O'Lantern' is not nearly as old as Halloween and originally had nothing to do with the holiday. 'Jack O'Lantern' was a 17th century term for a night watchman, so called because he carried a lantern on his rounds. The term was also applied to 'will-o'-the-wisps,' the strange lights sometimes seen in swamps and graveyards at night, based on the belief that the lights seen were the lanterns carried by spectral watchmen making their ghostly rounds. With such a spooky history, it's not surprising that Jack O'Lanterns became a fixture, and emblem, of Halloween.