This British term — much better known in Britain and Commonwealth countries than in the US — refers to the pulling of grotesque faces and has often been applied to that action as a competitive activity.
A surviving example is from the Lake District, where the Egremont Crab-Apple Fair has an annual contest, which they call the World Championship Gurning Competition and which they say dates back to 1266. There is also an Australian national competition that I know of, and there may be others, too.
At one time, such face-pulling contests were a common entertainment at fairs and gatherings around Britain (before the days of radio and television you had to get your fun where you could). The rules at Egremont are simple: competitors put their heads through a horse collar and then have a set time in which to contort their faces into the most gruesome, scary or daft expressions possible. False teeth may be left in or taken out, or even turned upside down if desired. The winner is the person who gets the most audience applause.
The word seems to have been originally Scottish, in the form girn, which — appropriately enough — may have been a contorted form of grin. It has had several meanings, of which the oldest — from medieval times — is still current in Scots and Irish dialect, and which is defined in the Oxford English Dictionary as: “to show the teeth in rage, pain, disappointment, etc; to snarl as a dog; to complain persistently; to be fretful or peevish”. These days only the losers in the World Championship Gurning Competition do much of that.