This type of bracelet takes the form of a spiral and ends in a snake's head. They were worn on the upper arm and are properly called armlets.
Roman jewellery borrowed heavily from Hellenistic goldwork. This particular type was common in Hellenistic times, especially in Egypt where these particular armlets might have been made.
Snakes were the symbol of a number of deities associated with healing, including the Egyptian goddess Isis and the Greek god of medicine Asclepios. It was therefore a commonly used pattern in jewellery, its spiral shape lending itself well to rings and necklaces. Worn as an amulet, the snake protected its wearer.