Final answer:
The hair papilla is the swelling at the base of the hair follicle that provides the hair with nourishment.
Step-by-step explanation:
The swelling at the base of the hair follicle that provides the hair with nourishment is called the hair papilla. It is a mass of connective tissue, blood capillaries, and nerve endings at the base of the hair follicle. The hair papilla supplies nutrients and oxygen to the hair root, promoting hair growth.