The upper pair of vocal cords (false vocal cords) are not concerned with vocal production; the lower pair (true vocal cords or vocal folds) can be made to vibrate and produce sound when air from the lungs is forced over them. False vocal cords typically do not vibrate. The false vocal cords sit above the true vocal cords and close for two reasons:
To protect your lungs from things going down the wrong pipe.
To create back pressure to cough something up.
Unfortunately, the false vocal cords often invite themselves to participate even if we do not want them there. In healthy singing we want them out of the way, i.e. open which is something a singer needs to learn. When we close the false vocal cords and sing or speak, the false vocal cords put pressure and rub on the true vocal cords. Ongoing pressure and rubbing on the true vocal cords can lead to injuries such as nodules.