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 often used interchangeably, although the former is more common when the opponents lead a suit. As a corollary, it's possible to execute a ducking play as declarer.
Examples
The classic example of a defensive ducking play looks something like this:
Dummy
Q82
J43
West
93
East
T94
KQJT9
AJ5
QT6
8752
QJT5
Declarer
8762
A76
K763
84
AK9
AK4
532
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:
Dummy
Q82
J43
West
93
East
T94
AQJT9
AJ5
QT6
8752
QJT5
Declarer
876
762
K763
K84
AK9
AK42
53
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.
See also
Count Signals
Defensive signals for showing the number of cards held in a given suit.
Ducking Play by Declarer
The intentional loss of a trick in a suit that declarer wants to establish.
Hold-up Play as Declarer
Declarer's intentional refusal to win a trick, in an effort to disrupt the defense's communication.
Q82
J43
93
KQJT9