A scarf is a wide piece of fabric that's worn around the neck or over the head. That long, warm, wooly thing you wrap around your throat in the winter is a scarf.
In the 1500s, a scarf was a "band worn across the body," from the Old French escherpe, "pilgrim's purse suspended from the neck." Today, a scarf can take many forms, from an itchy wool scarf to a head covering worn for religious reasons to a silk scarf tied jauntily around the throat. As a verb, scarf means "eat hungrily." You might scarf down some pizza, then put on your scarf and head back into the snow.