Definition of showdown value
The showdown value is when our hand is probably strong enough to win at the showdown(slaughter). Therefore, we don't need to bluff. If you are on the river in position and your opponent check and you have a small pair, you have a showdown value. Here, the small pair is probably not good enough to be bet on. 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 of a bluff, but since you have a showdown value (your small pair) and you have a good chance of winning the hand at the showdown a percentage of the time, it will be said that the player in the check-back position has a showdown value because he has a showdown value.
What if the situation is 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 your opponent is having 50% of the time a better hand and 50% of the time a worse hand. For this reason, your bet would accomplish nothing and you decide to go for a check. If your opponent bets, you will call because you have a showdown value, meaning your hand will be the best at knocking down a decent % of the time.