Definition
A value bet is a bet made with a hand strong enough to be called by worse hands — the goal is to extract maximum value from opponents who will call with losing hands. Correct value betting is the primary source of profit in poker.
Thin value bets are made with marginal hands that are ahead of an opponent's calling range by a small margin. Thick value bets are made with clearly superior hands against wide calling ranges. The size of a value bet should be calibrated to maximize the amount worse hands will call.
A common mistake is failing to value bet strongly enough with the best hand — checking the river with the nuts, for example, when an opponent would call a large bet. Another is value betting too thinly in spots where calling ranges are stronger than expected. Understanding what range of hands calls your bet in each situation is key to optimal value betting.
Example
You hold A♣A♦ on an A♥K♣7♠ flop — top set. Rather than slow-playing, you bet 75% pot. Your opponent is likely to call with AK (top two pair), KK, K7, and various other hands — all of which you dominate. Betting extracts maximum value.