The hair follicle is a small cup-shaped structure in the skin from which hair grows. The cup is lined with cells and connective tissue. It is part of the skin that grows hair by acking old cells together. Attached to the follicle is a sebaceous gland, a tiny sebum-producing gland found everywhere except on the palms, lips and soles of the feet. The thicker density of hair, the more sebaceous glands are found.