The term is a holdover from mechanical film cameras, where a rotating disc with a wedge cut out passed in front of the film. A half-open disc — 180 degrees — exposed each frame for half the time available. The convention survived because it describes motion blur more usefully than an absolute shutter speed does.
The 180-degree rule follows: set shutter speed to roughly double the frame rate. At 24fps that means 1/48, at 30fps 1/60, at 60fps 1/120. This produces the amount of blur audiences have been trained by a century of cinema to read as normal.
Breaking it is a legitimate effect. Narrow angles like 45 degrees produce staccato, hyper-sharp motion — the shredded, adrenal look of the Saving Private Ryan landings. Wide angles beyond 180 produce smeared, dreamlike motion. Both draw attention to themselves, which is exactly why they should be chosen rather than stumbled into.