A gnome is a mythical creature. In certain traditions and certain kinds of magickal practice, gnomes are elemental spirits of the element of earth. In other traditions, they are simply small, mischievous sprites or goblins.
Gnomes are often represented in small ornamental statues called garden gnomes, a German tradition. These are the target of a lot of pranks: people have been known to "return to the wild" these garden gnomes, most notably France's "Front de Liberation des Nains de Jardins" (Garden Gnome Liberation Front). Some kidnapped garden gnomes have been sent on trips around the world, being passed from person to person and photographed at different famous landmarks, with the photos being returned to the owner.
The GNOME desktop (GNU Network Object Model Environment) environment is a graphical user interface for computers running Unix-like operating systems, specially GNU/Linux.
One popular South Park episode features an organization of gnomes who gather underpants; see Underpants Gnomes.