Roughly speaking it is the amount of the pot you expect to earn from people folding (or the percentage chance that you will win the pot by someone folding).

e.g. In a $100 pot if you are considering making a $100 bet when you have a 45% chance of winning then it isnt worth it.

Since your EV is:

55% of the time you lose $100
45% of the time you win $100
EV = 0.45*100 - 0.55*100 = -$10


If however that bet also has 50% fold equity then your EV is:

50% of the time your opponent folds and you win $100
50% of the time your opponent calls
but 45% of this time you win $100
and 55% of this time you lose $100


Your EV is:
0.50*100 + 0.50*0.45*100 - 0.5*0.55*100 = $45

So fold equity can turn a losing bet into a winning bet. This is one of the reasons it is so important to be the aggressor in no limit holdem. It gives you 2 ways to win. You can win if your cards hold up but you can also win if your opponent folds.