Final answer:
The large structure at the base of the hair follicle is the hair papilla, which is surrounded by the hair bulb and its hair matrix that produce the hair strand.
Step-by-step explanation:
At the base of the hair follicle is a large structure called the hair papilla. This structure is a mass of connective tissue, blood capillaries, and nerve endings that nourish the cells in the hair bulb. It is key in the hair growth process as it is enveloped by the hair bulb, which consists of a layer of mitotically active basal cells known as the hair matrix. The hair matrix produces a strand of hair as these cells divide and hair is essentially a keratinous filament growing from this base.