Dentistry was the study and professional care of a person's teeth. A dentist was a person who practiced dentistry.
Most Starfleet medical personnel are trained in numerous fields, including dentistry. But there was also a dedicated sub-division of Starfleet Medical, Starfleet Dental, responsible for Dentistry. (DS9: "Paradise Lost")
In the 20th century, Maury Ginsberg was a very successful orthodontist in Scarsdale, New York. Orthodontics is the application of "braces" on a person's teeth, to realign teeth that would naturally fall out of alignment. (VOY: "Death Wish")
In the latter-half of the 20th century, time-traveler Dr. Leonard McCoy was sarcastically accused of holding a degree in dentistry by a surgeon preparing to operate on fellow temporally-displaced patient Pavel Chekov at Mercy Hospital. (Star Trek IV: The Voyage Home)
On Vulcan, a common dental practice is for a Vulcan to have their teeth coated in a trifluorinate compound to prevent cavities. Despite having this done in 2128, T'Pol had a cavity in one of her tricuspids that Dr. Phlox had to restore in 2151. (ENT: "Dear Doctor")