A value bet in poker means that you (or anyone else for that matter), are making a bet hoping that others will call to increase the pot. You are effectively attempting to maximize the potential value of a winning hand. In order for a value bet to be profitable, and hence worth making, you must have a positive expectation.
Positive expectation in this context means that for every bet you make, you will win at least more than one bet. Consequently, you usually make a value bet when you have a made hand as most made hands will win more than 50% of the time (or 100% if it's the nut). This kind of bet for value is usually seen on the river.
It is possible to make a value bet when you have a drawing hand. However, in this last case the rightness of making a value bet with a drawing hand will depend on the drawing odds and the expected number of calls. For example, we'll assume that the flop has just been shown and you're first to act. You hold 89 offsuit,
and the flop is K 6 7 rainbow :
You've hit an open-ended straight draw, so you have a fairly strong drawing hand. In fact, you have 8 outs and should make the straight 1 out of 6 times. So if you were to make a value bet here, you'd have to be called by at least 6 opponents to have a positive expectation, i.e.: you'll 6 bets once, and lose 1 bet 5 times, so +6 bets + -5 bets = +1 bet expectation.
How much should I bet?
The goal is always to extract as much as possible from your opponent, but that doesn't mean that you should bet the amount that you feel is the most likely to get called. For instance, let's reexamine our example above. Let's assume that you made the nut straight on the river, you're now heads up, and unless your opponent has 89 as well, you have the nuts. For the purpose of our example, let's say the pot is $50 and the minimum bet allowed $10. A rookie player might think that the best thing to do here is bet the minimum because it will increase the chance of being called. Okay, sure, let's say that 8 times out of 10, your opponent will call your $10 bet, as opposed to 2 times out of 10 if you were to bet the pot, $50.
8 times out of 10 you will win $10 extra = $80 in all
2 times out of 10 you will win $50 extra = $100 in all
As you can see, the most valuable and profitable play here would be to bet the pot, even if your opponent is 4 times less likely to call.
In conclusion, a value bet, is exactly that, a bet to increase the value of a particular hand and extract the maximum value out of it. Contrary to the float play or continuation bet the goal when betting for value is to induce a call from your opponent to increase the pot, because you have a positive expectation of winning.