Other forms: wagging; wagged; wags
A wag is a quick, back-and-forth movement. A scolding teacher might give you an irritated wag of a finger, while a happy dog will give you a cheerful tail wag.
Animals and people alike use wags to communicate various emotions, and when they do, they wag. Dogs are known to wag their tails in happiness or to express friendliness, but a very slow tail wag can mean a dog is uncertain or is trying to calm itself. Wag is at least partly rooted in the Old English wagian, "move backwards and forwards."