The vocal cords (or vocal folds) are thin folds of mucous membrane that are stretched from anterior to posterior across the larynx. The position and taughtness of the vocal cords are controlled by laryngeal muscles, and the vibrations produced as air moves across the vocal cords produces phonation (speech).
There are actually two sets of folds of tissue in the larynx. The vocal cords described above are sometimes referred to as the true vocal cords, to distinguish them from the false vocal cords (= vestibular folds). The false vocal cords are thicker folds of mucus membrane that sit just superior to the true vocal folds. Their role is mainly protective, they help keep food and drink from entering the airway.
Coronal section through the larynx to show the position of the true and false vocal cords.
Superior view into the airway to show the true and false vocal cords