An anvil is a large, heavy, metal environmental object with a flat top surface and a point on one end most frequently found on a sturdy block of wood or pedestal. An anvil is required for most Blacksmithing and Engineering recipes. You do not have to interact with the anvil, you just have to be in the vicinity of the anvil.
An anvil graphic is not necessarily a functional anvil in the game. Generally, a usable anvil will be selectable (but does not have to be selected).