Fold equity is most often used during the latter part of a tournament when you need to steal blinds. It can be considered a form of bluffing. If your opponent only has, say, 10 times the blind, and you have 30 times the blind and place a large bet, your opponent may fold because he does not want risk a large portion (or all) of his stack. His or her fold is basically a safety play in which they prefer to wait for a stronger hand.
Knowing when you have fold equity and don't is essential to it being successful. Fold equity is an estimate of what another player will do and should take into account the opponents style of play (tight or loose), the opponents stack size, how much they already have in the pot (be careful if an opponent is pot committed!), and your stack size and table image.
The main idea being using fold equity is to get your opponent to fold because calling your bet will be too expensive for comfort.
Find out more about fold equity in this video.