"I got top marks in Concealment and Disguise during Auror training without any study at all, it was great."
-- Nymphadora Tonks (OP3)
Metamorphmagi are born with the ability to change their appearance at will. The ability cannot be learned, and seems to be fairly uncommon, as the only known Metamorphmagi are Nymphadora Tonks and her son, Teddy Lupin. The ability also manifests itself right away – both Tonks’s and Teddy’s hair began changing color within hours of their birth. A Metamorphmagus’s abilities can be impeded by emotion; Tonks loses the ability for about a year when she is pining over Lupin.
There is certainly a genetic element to Metamorphmagus ability, given that Tonks passed it on to Teddy. But it is probably not as simple as a single gene - if the gene were dominant, either Andromeda or Ted Tonks would have had the ability, and if it were recessive, Teddy would not have the ability (unless Lupin was also carrying a Metamorphmagus gene, which is possible but unlikely).
The word comes from the Greek prefix "meta-" connotating change, "morph" meaning "form," and "magus" meaning "wizard."
A lot of fans thought Metamorphosing would be critical in Deathly Hallows due to the pattern of Jo introducing a new type of magic and having it be key two books later (Animagi in PS/PA, Polyjuice Potion in CS/GF, prophecies in PA/OP, the Pensieve in GF/HBP). That proved to be a red herring.