A value bet is a bet by a player who believes he holds the best hand, in hopes that one or more opponents will call.
With cards to come Edit
On betting rounds when there are more cards to come, you'll often be betting your good made hands and strong draws for value.
If you have a made hand your opponents could still draw out on you. In those situations, your value bet will often also serve the purpose of protecting your hand. That is, while you're hoping to get called, you're often going to be making it incorrect for your opponents to do so with their drawing hands. When they do call, as you hope they will, not only do you gain value but you have also gotten them to make a mistake by calling with incorrect odds.
There are going to be situations where you can't protect your hand, such as when the pot is very large in a limit hold'em game. Denying proper pot odds is very difficult sometimes. In those instances, you're value betting without the protection overlay. You still want to be called because you have an advantage versus a draw, but you aren't able to force that mistake on the caller.
Sometimes you're going to find yourself with the mortal or near-mortal nuts with more cards to come. You may have a straight flush with a blocking card or top quads. In those situations you want to extract maximum value. Whether you're value betting or slowplaying depends on your opponents and whether you think they have hands good enough to give you the value you want.
With no cards to come Edit
On the river, all the cards are out so there's no motivation to protect your hand anymore. Now the goal of the better hand is to extract value, pure and simple. For more information see LHE:River:Value bet and NLHE:River:Value bet.