Vasuki is the king of the nagas, and is often depicted coiling around Shiva's neck. He is brother of Sheshnaga & the son of Kashyapa and Kadru, and the grandson of Brahma, the creator of the universe. Vasuki is also known as the king of snakes and is depicted with 1000 heads.
Vasuki's three coils represent the cycle of life in terms of time. His head, which is always positioned on Shiva's right shoulder, symbolizes Shiva's everlasting justice and laws to preserve the nature and order of the universe.