According to old tales, these Pokémon are stumps possessed by the spirits of children who died while lost in the forest.
(From  Bulbapedia) Phantump is a child's spirit possessing a rotten tree stump, and lives in abandoned forests. It is a wispy, grayish black Pokémon. A small tree stump covers its head, with a single, wavy branch situated on either side and extending upward. Each branch has two small, green leaves near its tip. Phantump's red, oval eyes are visible through two holes in the body of the stump. On its body is a pair of tiny, stubby arms and a wispy tuft on top of its head. Its mouth appears to be on the stump itself rather than on Phantump's body.
It is said that in forests where humans seldom tread, the stumps of the very biggest trees become Phantump. People that happen to enter the forest may be led astray by Phantump, as they are capable of imitating the sound of children's voices. Phantump along with its evolution Trevenant are the only known Pokémon capable of learning Forest's Curse.
(From Bulbapedia)Phantump is probably based on the stump of a kodama, the spirits of trees that sometimes inhabit old aged trees. It is also similar to other types of tree and nature spirits and deities, such as dryads. Its Shiny coloration is based on the birch tree, known for its gray-and-white bark, with its leaves representing a tree in the autumn.
(From Bulbapedia) PPhantump may be a combination of phantom and stump.