An overcall refers to calling after someone else has called a bet. For example, after the flop an early position player bets. A middle position player calls the bet. All further calls would be considered overcalls since they call after the first caller. Preflop, we don't refer to limpers as overcallers.
So, why do we need a term for this? It's just calling, right? Well, there are strategic decisions involved in overcalling.
First, you need to decide whether you will overcall. There's a bet and a call before you. If you suspect the bettor is bluffing and you think you can beat him, you might normally call, but to overcall is pointless since the caller isn't bluffing. On a related note, if you decide to overcall you must keep in mind that you are now having to beat two players, not just one. You need a pretty good hand to overcall. You'll often hear something like this at the poker table: "Well, if you're calling, I guess I'll fold". Someone who says this understands the difficulty in being the overcaller.
There is another instance where overcalling comes into play, and this time you can use it to your advantage. When you make a strong hand in a multiway pot, you need to think about playing strong by raising for value versus sandbagging a bit and hoping for overcallers who may pay you off all the way. Let's say you hold a full house after the river card has been dealt. There's an early position bettor who has been going strong the whole way. And there are two players after you who have called along, possibly with two pair. At the river the early player bets, as usual. You now have a decision to make. Do you raise or call? If you raise you will probably lose the players behind you and you'll likely be called by the bettor, gaining one more bet. If you call, you may get overcallers which would net you two extra bets with your monster hand.
There are a couple things to think about when trying to get overcallers. Do you have a real monster that can withstand multiple people calling you? Remember that by going for overcallers, you have no fold equity. Also, if you don't think the players behind will call, based on how they've played up to that point, then you'll lose money trying for the overcallers.