A hair follicle is a part of the skin that grows hair by grouping old cells together.
In 2365, Dr. Katherine Pulaski advanced in age and became elderly. A hair follicle of Pulaski was used to take a sample of her genetic code so she would be reverted back to her original age, via the transporter. (TNG: "Unnatural Selection")
In 2369, a Bajoran named Ibudan was found murdered in one of Deep Space 9's holosuites. Dr. Julian Bashir scanned the holosuite for hair follicles, hoping to find the culprit of Ibudan's murder. (DS9: "A Man Alone")
Alfarian hair pasta is made from the hair follicles of a mature Alfarian. The follicles are harvested by Talaxians during the Alfarian's shedding season in early fall. (VOY: "Parturition")
In 2379, Dr. Beverly Crusher speculated that Shinzon was cloned from Jean-Luc Picard by using a hair follicle or a skin cell. (Star Trek Nemesis)