When you would like you opponents to call your bet (as opposed to you bluffing). This bet is typically smaller which helps keep others in the game. Typically you have the nuts or a high favored winning hand.
A value bet is made purely for profit-- most commonly on the river when you are no longer betting, at least in part, to protect your hand as you would be on flop and turn. Another example of a value bet might be betting into a large field (four or more players) on the turn when you're on a flush draw. You really want to be more than fifty percent sure that your hand will be good, if called, to bet for value on river.