Definition of showdown value
Showdown value is when our hand is probably strong enough to win at showdown. Therefore, we don't need to bluff. If you are on the river in position and your opponent checks and you have small pair, you have showdown value. Here, the small pair is probably not good enough to bet. Also, if you bet, your opponent will never fold better than your hand and will rarely call with worse. If you had nothing at all, you might think it was a bluff, but since you have showdown value (your small pair) and have a good chance of winning the hand in the showdown a percentage of the time, the player in position would be said to check-back because he has showdown value.
What if the situation was reversed?
If the situation had been reversed on the river, the thinking would have been the same. This time you are out of position with a small pair. You suspect that your opponent has a better hand 50% of the time and a worse hand 50% of the time. For this reason, your bet would accomplish nothing and you decide to check. If your opponent bets, you will call because you have showdown value, i.e. your hand will be the best at the showdown a decent % of the time.