A ladder-breaker (shicho-atari in Japanese) is a stone that prevents a successful ladder.
It may be an existing stone on the board. Or it may be a play made after the ladder has been set up - in the latter case, the player who has the ladder must decide whether to complete the ladder capture, or answer the ladder-breaker. This can be a serious dilemma.
See ladder for more basic information.
There are certain plays that are a long way from being part of joseki, and which are expected only in the context that they are ko threats or ladder-breakers.
Ladder breaker or ko threat
For example here is much too violent to be useful as an approach move: the
stone will suffer from a local disadvantage if Black answers here.
On the other hand if Black has to ignore for tactical reasons, and White can play hane next at a or b, White will have the upper hand locally here.
There is an overlap between plays that make good ladder-breakers and those that are good ko threats, therefore. And if these plays are ignored, the same sorts of local follow-ups will apply. In general fighting a ko is much more complex in its implications.
There is a difference, though, when one considers what the other side (Black in this case) can do to resist. In the case of ko fights, answering is just what the opponent counts on.
Here it would depend on the actual ladder whether made the ladder good again for Black. If White continued at c in another attempt to break the ladder, the game will undoubtedly become difficult. These resistance fights are hardly mentioned in books: probably they are an aspect of pure strength.