The arytenoid muscle or cartilage is located behind the larynx that the vocal cords are connected to.
The arytenoid muscle or cartilage is involved in opening and closing the vocal folds for both breathing and talking so the arytenoids muscles or cartilages are pretty important.
These muscles allow the vocal cord and folds to relax or tense as needed. How relaxed or tense the arytenoid muscle or cartilages are directly affects the vocal cord muscle and how a person sounds when talking, singing and even affects breathing.
The arytenoids cartilages or muscles move inside the cricoarytenoid joints while breathing and talking and the arytenoid helps with the opening of the vocal cords.