The suffix -ist generally refers to a person who specializes in or practices a certain field or profession. In the case of the word orthodontist, the suffix indicates that the person is a specialist in orthodontics, which is a branch of dentistry focused on diagnosing, preventing, and treating dental and facial irregularities.
As for the part of speech, the suffix -ist typically converts the base word into a noun. Therefore, orthodontist is a noun that refers to a person who practices orthodontics.