Basically equity is your expected winnings given your and you opponents' hands, if the hand is played to showdown. I.e. the chance of each outcome multiplied by the amount won in each case, added together. It's usually expressed as a % of the pot.
- If you have the winning hand on the river, you have 100% equity in the pot.
- If you're on the flop, and you have 5 outs to win the hand, you have about 20% equity, because you will hit one of your outs about 20% of the time if played to showdown.
It's not always equal to your chances of winning, since it's a bit more complicated to work out in hi-lo split games, and in other games when you stand a chance of splitting the pot, but it's still equal to the mathematical expectation of your winnings.
Fold equity (as opposed to "pot" equity) is just the part of your equity for the outcome where you bet and your opponent folds. I.e. the chance of them folding x the size of the pot.
E.g. You have a flush draw and shove the flop. You are behind but have 9 outs. So you have 35% equity, but you also get extra equity (expected winnings) because your oppontent folds and lets you take the pot some % of the time.
It's difficult to work out your exact fold equity (a definition is here (http://www.google.com/base/a/1121639/D14649816285364122504)) because you win less when your opponent folds than if they call and you win.