Fold equity is the value you hold in a pot due to the likelihood that your opponent will fold on a current or future street. Obviously fold equity can only be realised if you bet or raise, but it is worth noting also that a "bluff" bet is not always wasted if it is called, since the bet can increase the likelihood of a fold on future streets - i.e it increases future fold equity. Obviously all of this is dependent on the profile of the villain - there is little or no fold equity if he is a calling station. Fold equity is also obviously higher with fewer players in the hand.
Fold equity is a partner to showdown equity - which is the value you hold in the pot due to the likelihood that you will have the best hand at showdown. Pot odds and "outs" calculations are all based on showdown equity. The way I think of it, fold equity is mutually exclusive with showdown equity. That is, I only count towards fold equity value which is due to somebody folding a hand which could beat me at showdown.
In many situations in limit holdem (especially shorthanded), the fold equity in a pot can be very high. If you are the preflop raiser, continuing to bet (Cbet) on the flop, the turn or even the river can be justified even if you have no hand. In fact, there are many boards where I would bet the river with no hand but would check-call with a stronger hand like 2nd pair or top pair no kicker (see the previous strategy note).
Here is an example from the other night:
***** Hand History for Game 2227734165 *****
$2.00/$4.00 Limit Texas Hold'em - Sunday, October 19, 10:12:53 ET 2008
Table Act Naturally (Real Money)
Seat 6 is the button
Seat 1: Rayon ( $209.60 USD )
Seat 2: trainee1 ( $84.30 USD )
Seat 3: dixxi ( $96.20 USD )
Seat 4: Hero ( $77.00 USD )
Seat 6: bigboss1977 ( $279.41 USD )
Rayon posts small blind [$1.00 USD].
trainee1 posts big blind [$2.00 USD].
Dealt to Hero [ 8s 7s ]
Hero raises [$4.00 USD] (I used to limp hands like this, now I very rarely if ever limp to open)
Rayon calls [$3.00 USD] (a moderately tight player)
trainee1 calls [$2.00 USD] (a LAG, but one who seems to only push it when he is in the betting lead)
** Dealing Flop ** [ 3h, Jc, 6s ] (whiff)
Hero bets [$2.00 USD] (here I nearly always Cbet unless the board is scary)
Rayon calls [$2.00 USD] (no checkraise, so he is weak at best)
trainee1 folds (great, the LAG folded)
** Dealing Turn ** [ Kh ] (still nothing for me)
Hero bets [$4.00 USD] (pot is now $16, so I only need him to fold 1/5 of the time for this bet to be worthwhile)
Rayon calls [$4.00 USD] (darn)
** Dealing River ** [ 3d ] (I have absolutely no hand - my showdown equity is practically zero)
Hero bets [$4.00 USD] (pot is $24, so I only need him to fold 1/7 of the time - a bet here is justified against most players)
Rayon folds (bingo!!)
Hero wins $26.80 USD from main pot
There is a fine line between solid aggressive play and turning into a maniac. You need to choose your spots carefully - if you pull this too often, your opponents will catch on and start calling you down with light hands.