Used properly, the holdup is a key strategy in declarer play.
When you start to play bridge, the first thing new players learn is that taking tricks is good. This is true, but you have to be selective in the tricks you take. If you lose the first four and win the last nine, that is just as good as winning the first nine tricks.
Alternatively, if you lose two tricks, then win two and lose one, then win five, lose one and then win two and lose the last, that totals nine tricks and is just as good a result as winning any other combination of nine tricks.
It usually takes a while to learn that if the goal is nine tricks, it does not matter which nine are taken. The next thing to learn is that in some cases, you must lose some tricks along the way in order to maximize the chances of making your contract.
Here is one simple example. Assume you are playing IMPs, where making your contract takes precedence. By contrast, in matchpoints it may be reasonable to jeopardize your contract in search of overtricks.
You reach 3NT as South and you get the lead of the ♠Q, the major partner bid. This is a little annoying because it has hit your weak spot. Do you win this trick? If you play low, East will play the ♠7.
If you win the ace at trick one, you better guess the clubs because there is some chance that letting the opponents in will allow them to cash too many spades. Your correct play is to let them win the first trick. You will notice that this contrary to instinctive play, which is to win tricks. After all, if the clubs run, you will have at least 11 tricks. It is easy to find a reason for greed.
So you duck, and West continues with the ♠J. Should you win or let them hold the trick? Again, you duck. East plays the king on this one.
While you may lose one trick by holding up, you ensure making your contract. Do you see why?