There is a saying in Yoga that if you can control the breathing, you can control the person. Think about this for a moment. If I could make you breathe hard and fast and shallow for a couple of hours, I could probably induce in you a nervous breakdown. So let us apply this idea to the voice in acting.
From a purely technical point of view control of the breath is absolutely essential for anyone who wants to be a real actor. To begin with, there are long speeches in plays, particularly in Shakespeare. We all take pauses when we are telling a story for instance, but the pauses tend to be automatically regulated by the stages in the story, or perhaps, the dramatic effect that we want to create. However, in Shakespeare, there are some speeches that may be equal in length to you counting up to 80 in one breath, without any obvious place for a pause to take a breath. The trained actor must be able to handle such a speech, but this will only be possible because she has undertaken full voice and breathing training.
Returning to our original claim, the way you breathe can be intrinsic to the character you are playing. Someone who is quick and nervous, or stressed, may well breathe in short rapid breaths. A slow, ponderous or dull-witted character would breathe in the opposite fashion. The best example of this is seen in many of the films of the famous English comic actor, Peter Sellers. He changes his breathing rhythm according to the character he is playing. (He also changes the way he walks, as do many other actors). Few other actors change their breathing. If you get the chance, compare Sellers in The Waltz Of The Toreadors and, perhaps, Heavens Above, or Only Two Can Play or I’m Alright Jack. In The Waltz Of The Toreadors, Sellers plays a retired army major who is overweight, drinks too much and can’t keep his hands off the maids in his household. As he trundles round the place, and trundles faster after the maids, his breathing patterns become obvious.
So, from the point of view of both physical capacity, and characterisation, both breath capacity and breath control are essential tools the actor brings to fashioning a role.