In the card game of contract bridge, to hold up means to play low to a trick led by the opponents, losing it intentionally in order to sever their communication.
The primary purpose is to give as many tricks to opponents as needed to exhaust all the cards in the suit from one of their hands.
Assuming there are no side entries, on the distribution shown East must duck once to prevent declarer from running the suit.
If West signals an odd count, East will have to decide (possibly from the bidding or previous play in other suits) whether it shows three or five, and win the first or third trick accordingly.
Here is a simple endplay situation: NW ES At no trump, South is on lead with three cards left to play.
If West takes the ace, the declarer could easily play the king in second round, dropping East's jack.
If there were an additional diamond in either the North or South hand, for a total of six, then declarer need only duck one trick (winning the second).