Dogs will wag their tail to convey various emotions: happiness, nervousness, feeling threatened, anxiety, submission, and excitement. Studies have shown that the pace and position of the wag will often convey emotion. If a dog is frightened or submissive, it’ll often hold its tail down and possibly wag it a little between its legs. Dogs that are alert or excited will hold their tail higher than their natural position. Often this high tail will be wagging furiously – a fast-paced wag will often mean a dog is happy or excited.

Source: The Healthy Pet Club