1. A pair that's weak under these particular circumstances. It could be top pair with a weak kicker or bottom pair with a good kicker (why not bottom pair with a weak kicker? Because you don't continue with hands that bad)! You could have a pocket pair that is beat by the board, but you don't think it paired any of your opponents' cards.
2. A straight- or flush- draw.
Let's look at some examples of these types of hands:
You're in the blind with K¥5*. The flop is K*9*3V. There's a bet and you raise.
The other player will often check to you on the turn. If you like the turn card, or it improves your hand, or you feel that your pair of kings is the best hand, regardless of kicker, then you can bet it again. If the turn card doesn't help you, and your opponent checks into you, you can check and save a big bet. If it then turns out that your opponent had you beat with, say K>84, then you got a free card when you had the worst hand. Drawing for free with the worst hand! It doesn't get any better than that, and it happened because you raised to get a free card.
You have A434. The flop is JV6*34. There's a bet and you raise.
If the bettor checks to you on the turn you can also check and see the river card before you have to put any more money in the hand. If you spike another ace or 3, you'll have gotten in an extra bet with a winning hand, which is the essence of all forms of poker. If you miss on the turn and the river, you will at least have gotten to see the river for free.
If you repeat this situation over and over during the course of a game, occasionally you'll hit your hand, and you'll win much more than the cost of that little $3 raise on the flop. There's also the possibility that your small pair is the best hand at the showdown, and you, then he's telling you the opposite. Pocket aces and kings are two hands with which no one should mind reraising a sole opponent before the flop.
If he reraises, then you can put him on pocket aces or kings. If you know your opponent is a little looser than most, you might want to give him credit for pocket queens or jacks or possibly AK suited.
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