An ARC break is a situation characterized by a significant, generally sudden, drop (break) in Affinity, Reality and/or Communication. A non scientologist would recognize this as an upset or as becoming pissed off at or about something.
Example: Dick and Jane's date is going marvellously, grins and green flags in both directions. Inadvertently, Dick comments about how much he despises the music of the Beatles (which happens to be Jane's ALL TIME favorite group in the universe.) Suddenly, Jane turns cool. Jane has had an ARC break. Specifically, something came up that is not real to both of them. This initial decrease in reality (sometimes called an R-Break) leads to a corresponding decrease in Affinity and - unless Dick gets a clue and remedies the situation - will lead to a diminishment of Jane's willingness/desire to communicate with him which will further decrease their mutual reality and affinity in the manner of a downward spiral.
Organizational Example: Mark has come into his local Scientology mission seeking some auditing. The registrar, Brad, is very aggressive in trying to help Mark come up with the required tuition, he shouts at Mark more than once and reads to him, very loudly, the Scientology definition of reasonableness within earshot of the receptionist Dianne, who is new to Scientology. After an hour or so, Mark is convinced he should just man up and ask his father to loan him the few grand his services will cost. He thanks Brad for helping him past his reasonableness and he is all VGIs as he leaves. By this time Dianne has gone home. She does not return the next day. Dianne has had an ARC break. Mark is a nice old man and Brad was mean to him. Scientology maybe isn't for me she thinks. Even though Brad did the yelling and Mark recieved it and was ultimately Ok with it (because it is real to him that sometimes he needs to be yelled at so he gets past himself), an ARC break has occured. Unless this ARC break is uncovered by someone and repaired, Dianne will likely end up in the Freezone (joke).