A snake that bites its own tail is called ouroboros. The ouroboros is a symbol of eternity, and represents the cycle of life, death and rebirth that lead to immortality.
As it appears in the Encyclopedia Britannica, the ouroboros is a gnostic and alchemical symbol. It also expresses the unity of all things, spiritual and material, that never disappear but perpetually change in a constant destruction and rebirth cycle. Crystalinks cites that Carl Jung found the ouroboros to be of archetypal significance to the human psyche. Jungian psychologist Eric Neumann views the ouroboros as a representation of undifferentiated infancy experiences in both mankind and individual child.