The poker term “betting for value” applies only to a bet made after all the cards are out. No longer is there a need to protect your hand, and the sole purposes of a bet are to either make an opponent fold who has a better hand (a bluff) or collect more money from a worse hand (a bet for value). We usually use this term only in describing a situation where there is some doubt whether your hand is good or not, so you have a decision whether to check or bet depending on whether you believe your hand is still good.
Many holdem poker players need to adjust their mindset a little in river betting. Their attitude when they have been carrying the betting seems to be, “I have protected my hand to the maximum; now let’s see if it is the best.” Then they check a decent but unspectacular holding. The more aggressive and more profitable attitude is, “At limit poker, the opponent is likely to call on any pair just to see if I have been pumping on some kind of a draw or overcards, so I have a chance to make more money if I have a real hand.”
The way to make that extra money at limit holdem is to realize that the normal place for an opponent to make a move is on the turn, not the river, if they have a hand that looks like it should be good (as opposed to hitting on the end). There are many times when you bet the turn with your heart in your mouth, because the turn-card is of some danger, but you do not want to give up the initiative and allow a free card. Here is an example to dramatize such a situation.
You have pocket queens and raise the pot, getting called by the button and the big blind. The flop gives you an overpair without any particularly threatening card combination. We will use Jc-8d-5h as an example. The first player checks, you bet, and they both call. The turn is the Kc. The first player checks again. An overcard is never welcome, but you grit your teeth and bet again. Only the player who checked calls. On the end comes another king, and he checks. What should you do?
The first thing you should realize is you have caught a good card for your hand. It is impossible that the player drew out with that second king. It is even better than catching an innocent-looking deuce. If by some miracle the opponent had two pair on the turn (with a king not one of the pairs), you are now back in the lead. If the turn king had hit him, he would likely have either led into you on the turn or check-raised. Since he did neither, and also checked the river, it is clear to bet again and collect one more big bet for your reward. He does not know you have Q-Q, and if he holds a pair, will probably pray you had A-Q and pay you off.
This theme of catching an overcard on the turn and having it pair on the river comes up over and over again at holdem. Make the most of it when the betting action indicates your former top pair or overpair that you had flopped is still good. Bet for value.