The vocal cords (or vocal folds) are located in your larynx (voice box).
When you ‘vocalise’, air from the lungs passes the vocal cords and they will start vibrating. This vibration produces sound.
The vocal cords can be stretched to make higher tones. They can also become thicker and thinner. Most people speak with thicker vocal folds. When you sing, thinner vocal folds are much healthier.
We have two pairs of vocal cords, false and true vocal cords. We make sound with the true vocal cords. You can also make sound with the fals vocal cords, in some musical styles they are used for grunting and other distortion. Many times the false vocal cords constrict the throat. To prevent that, you can use the inner smile technique.
The true vocal folds, the ones that make the music, react to the amount of air that passes. That is why breath support is a very important element in vocal technique. Breath support is about managing the airflow, if you do it right your vocal folds will receive the perfect amount of airflow they need to vibrate freely.
This video shows the vocal cords/folds of 4 singers while singing.
The epiglottis that you can see below the vocal cords in the video produces TWANG when the epiglottis closes over the vocal cords.
You can see that not all four singers use TWANG in the same amount.
These four classically trained singers all use relatively thin vocal folds. You can read more about the vocal folds while singing in the article Thin and thick vocal cords.