Canon breaks are visual or visceral phenomena encountered by agents in a Word World when severe errors or damage to canon are made in badfic. Canon is the default substance of the Word World: its bones and base elements. If canon is changed without well-developed substitute elements also being introduced (say, in AU goodfic) then the world of a continuum really does begin to cease to exist—the world can be said to be 'broken.' Thus the name: canon break.
If character rupture can be said to be the point where a canon character would never be able to fulfill his canon role, canon breaks are the equivalent for an entire world. If they go unchecked, canon breaks will cause canon damage.
It is a primary task of agents to repair canon breaks, which can usually be done by eliminating the uncanon disruption breaking the canon. When the inserted uncanon material is destroyed, the canon usually is quick to spring back to repair things... usually. FicPsych exists to repair characters that are too broken to be fixed by a field neuralyzer, and sometimes other crews (such as DOGA) are required to completely correct really atrocious and wide-reaching canon breaks.
When on a mission, agents must wait for the first major break in canon to step in and begin their work—otherwise, they have no reason to be there, for the fic is not a really offensive one. An inconsistent level of unreality (such as a single charge of impossible ancestry) is not enough; a specific canon-shattering event is usually needed, or a major pileup of disruptive charges. This is usually why a long list of charges both minor and severe is required before a Mary Sue can be eliminated.
A considerable break in canon will cause everything in the Word World to seem 'a little off' even before the cause can be detected. A severe break in canon may cause the world to be out of focus or be distorted. An extreme break in canon may shatter the world entirely and replace it with one made out of generic surface, or even an urple world depending on the nature of the break. In one case, a complete canon break caused the entire world to freeze and nearly killed the four agents in the fic at the time.