This phrase is used when one finds themselves in a situation of intense irritation by another party. The feeling is so intense that even the mere breathing of the aforementioned third party is considered infuriating.
Tom says, "I can't believe that she got employed."
Mike replies, "I know, right. Can't believe it either. It's like the company wants to employ idiotic people. I CAN'T STAND HER!"
Tom replies back, " Watch that bitch breathe ... "