On defense, "ducking" or "holding up" means to purposely refrain from taking a winner. The purpose to disrupt declarer's communications. In bridge parlance, the terms "hold-up" and "duck" are generally used interchangeably, although the latter is more common for the defense. As a corollary, it's possible to execute a hold-up play as declarer
The classic example of a defensive ducking play looks something like this:
Declarer is playing 3NT, and West leads the Q. Declarer wins the A in hand and leads a low club toward dummy. If West takes his A immediately, then declarer can score four club tricks in dummy. However, if West holds up his ace for two rounds, then declarer can only score two club tricks.
How does West know when to take his ace? He should be watching for a count signal
by East in clubs.
A ducking play can also occur when declarer attempts a finesse. We change the hands slightly to arrive at the following layout:
Again the contract is 3NT and West leads the Q.
Declarer wins this in hand and tracks a low club toward dummy. West should follow with the 2,
a count signal
indicating an odd number of clubs.
When declarer finesses, East holds up the K.
This entices declarer to lead a heart back to his hand and try a second finesse. Now East takes his king, thus limiting declarer to only one club trick.