"Level breaking" is a term used mostly by drama-geeks to refer to an event in a script or an uneven portrayal in acting that wrecks the intended emotional tenor of a scene or an entire piece.
In portrayals, when actors take it too big (start Chewing the Scenery, rending the wardrobe, inserting pratfalls, etc.), they are level-breaking by going "over the top." If they play it too flat, they are breaking by way of "phoning it in."
It is much easier to level-break by going over the level than it is by going under the level: a person not displaying their emotions is less challenging to the viewer's Willing Suspension of Disbelief than a person... well, behaving like an actor.
You can, given the proper medications and directorial blandishments, eventually get an actor to either calm down or wake up. (Well, most of 'em, anyway.) In scripts, the problem is a little harder to pin down.
The most common level-breaker in a script is a Mood Whiplash, a jump from way-sad to way-ridiculous. The 'breaker is in the "way-" part, in the degree of emotion. Having a détente scene, something to break the tension a little after a sad bit is not a bad move, but it has to be done with some care.
This can also apply to other media, such as an immersive game being interrupted by an intrusive user interface, or a serious Deconstruction Game about shooters being interrupted by an achievement notification after mowing down dozens of Mooks in a row.
This defines the fan-speak term. No examples are wanted. They have a tendency to drift into bashing.