A grotesque carved human or animal face or figure projecting from the gutter of a building, typically acting as a spout to carry water clear of a wall. Yes there's your answer. Ugly scary old things!
Like Rooster said. It's a demonic statue in the Grotesque style in Gothic architecture that was used to act as rain downspouts. If it isn't a downspout it's called a chimera and if it is a relief in the wall it's called a boss.
Ah, no ... A gargoyle is nothing more than a rain spout on a medical building ... Designed to shoot roof run off away from the building ... Then they started decorating them ...Ok ... I'm a pedant so sue me lol