Whenever I teach I always remind the students to breathe, because they tend to forget it when being very concentrated. In addition to the obvious getting rid of CO2 and refilling O2, they also get less tense when breathing properly.
For performers, the breath has a very large impact on the emotions you are projecting while on stage as well as giving certain moves an extra impact. Some of my previous teachers have had some focus on it, but the real difference for my awareness of my breathing on stage while dancing was after I joined a workshop with Ranya Renee some years ago.
It has made a difference on my dancing, and I've also realized that if I use my breathe as a tool the audience will unconsciously breathe with me.