A bet is when you make a bet.
A raise is when you raise someone else's bet.
A re-raise is when you raise someone else's raise.
Obviously, the re-raise is a very aggressive play. You're saying "I don't care that you think you can beat my hand". But is it a good play?
Sometimes.
Let's deal with Limit Holdem first.
Re-raising is a good idea pre-flop when you hold a monster (that's poker talk for a very strong hand - AA, AK, KK, and maybe QQ). Why? Because it gets more money in the pot when you are likely to have the best hand, and reduces the number of hands that your opponents are likely to play against you (so you can feel more confident that the second 4 didn't give your opponent three of a kind)
Re-raising usually is a bad idea on the flop. Why? Because it says that you are very confident in your hand, it means you are less likely to be raised on the turn (when the bets double) so you are likely to be costing yourself half a bet.
Re-raising on the turn can be a good idea. If you've just called (or bet and called) on the flop, and the turn card either helped you or was a scare card (a card that could have completed a draw), then re-raising here will either drive your opponent out or squeeze them for another bet.
Re-raising on the river should only be done when you're almost certain you're the winner. Most opponents will almost always call, and there's no more cards to come.
No Limit is a different game entirely when it comes to re-raises. Because there's no limit to the amount you can bet, a big re-raise at any stage is sometimes the best play.
If you're going to be re-raising in No Limit, you want to be going big. Don't just make the default raise. The bet should be at least as big as the pot (including your original bet and your opponent's raise). This is obviously a big play, and you need to be very confident in your bluff or your hand.
I've written another entire article about going all in, because it's that important (and enjoyable) a topic.
But in summary, be very sure what you're doing when you re-raise.
