I don't know if this topic is still active, but I thought I would reply to the excellent explanation by NReilingh from 2013.
I had the great honor and opportunity to sing under Dr Ernest G. Sullivan, PhD, at Alma College during the 1970's. We performed as an a cappella chorus of about 60 voices and in a madrigal group of 10-12 voices. Dr. Sullivan, who was a vocal music purist who did not prefer to mix voice with orchestral instruments (with the exception of the organ) generally used a baton with the chorus, holding it in his right hand.
At the same time, he used his left hand to do what he called "shaping". I must add that he was completely ambidextrous, having been a trained organist as well as vocal performer. So it was imperative to pay attention to both his baton and his left hand, since they were communicating and directing two separate messages.
He felt that the voice was the most versatile and expressive of all instruments, and used his left hand to direct changes in tone like timbre, pitch, intensity etc. He also had hand signals for embouchure such as vertical, elongated, throat shaping and the like. Also, the left hand provided his guidance on breath control, one of the main factors the he believed separated good choirs from great ones.
However, with the smaller madrigal group he used only his hands, and trained us to do the same. Any one of us could, as necessary, direct the madrigal singers as dictated by the piece, the venue or other factors.
I was never talented enough to be a professional performer, but many of my classmates were. I did learn, however, to trust Dr Sullivan's instruction. I do encourage musicians who aspire to be conductors or directors to learn to use the baton, as well as develop their hand skills, as did Dr. Sullivan.