A fang is a long, sharp tooth that is used to do harm. Vampires have them, venomous snakes have them... you could have them, too, if your Halloween costume includes a set of pointy teeth.
The word fang came into English from the Old Norse word fang, meaning “capture, grasp.” It was originally used to describe something that was seized or captured, like loot taken after a battle. Later it meant "something that traps or snares." When you think of a sharp tooth’s ability to snare something, it’s not such a leap to the word’s current meaning: the long, pointy teeth of a predatory animal or a snake — or a vampire.