The Pencil Eraser will erase an iron pencil-shaped statue which is preventing the player's progress in seversl points of the game. There are three iron pencil statues in the game: in Peaceful Rest Valley, the Monkey Cave and Winters. Of these only the one in Winters is optional to remove, as it is solely blocking a shortcut to skip Brick Road Maze.
In Mother 3 there is only one pencil statue in the game, being the one on the 100th floor of the Empire Porky Building. The Pencil Eraser is beside the statue and can be used to erase it, however it is mainly a novelty item as the statue is not preventing progress.
In Japan, the item is known as the Octopus Eraser which erases octopus statues. This is a play on a common phrase in Japanese gaming culture where if a player feels stuck with no way to advance, an octopus is blocking the path. Its English name is intended to be a pun on "pencil eraser", which refers to the eraser on a pencil, but is instead an item that erases pencils itself.