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Pot equity is your percentage chance of winning the pot at any given point in a hand. That percentage is the amount of equity you have in the pot or how much of the pot "belongs to you".

Here's a Texas Hold 'em example. You hold AsAh and you have a single opponent with what could be any hand. Your pot equity against a random hand is about 85%, meaning that if you both pushed all-in and the hand went to the showdown you can expect to win about 85% of the time. Notice that this is for a run all the way to the river with no strategy discussion and no chance of anyone folding to scare cards. The effect is the same as if both players agreed to check all the way. Pot equity does not tell you anything about numbers of bets you can expect to win.

You're not always up against a random hand, of course. If my opponent calls my raise with my AsAh above, I can start to put her on some hands which will eat away a bit at my pot equity.

You probably won't be figuring pot equity at the table. You'll mostly be figuring it after the fact when you wonder how good your AKs was against someone's ATo (answer 75%). Use a tool such as PokerStove for help in figuring your pot equity.

Pot equity has some use at the table. Primarily it lets you know how much of the pot "belongs to you," as mentioned above. When you know your equity, you can compare it to your "fair share" which is just the pot size divided by the number of people in the hand. So, when you start a hand with pocket aces and have three opponents, you know that your fair share is about 25% but your pot equity is around 85%. Therefore, all bets that go into the pot earn you more than your fair share. This is especially useful when you're trying to determine whether to check/call vs. bet/raise with a flush draw. If you have many players in, your pot equity (the chance you'll win the hand, which is directly related to you making the flush) vs. your fair share may warrant a bet/raise rather than a check/call. That is, every bet you put in and get called is, theoretically, extra money for you when your pot equity is higher than your fair share.