The Vampire Plant's name was given to it by the characters of the original Mothra film. The "vampire" part of its name probably means that it kills people and animals and eats them, and the "plant" part of its name comes from the fact that it is a plant.
The Vampire Plant's vines have a purple color to them. They look much like normal vines outside of that.
The Vampire Plant was mutated due to atomic testing on Infant Island.
When Shin'ichi Chūjō was exploring Infant Island on his own, he comes across mutated flora. As he passed through the low hanging vines, the plants attacked him, squeezing him to unconsciousness. Before passing out, the last thing he sees are the Shobijin, who save his life.
The Vampire Plant has constricting vines, which are used to squeeze the life out of its victims.