With breathing squats, you take 3 deep breaths between each rep, which roughly constitutes a 10 sec pause, making this, essentially, a rest-pause set (more like 20 sets of 1 than 1 set of 20), which allows for larger motor units to be recruited for a longer period (they get time to partially recover between reps). But you should remember that it's brutally hard and works for a relatively short time (adaptation comes soon).
