There are many explanations of this ancient symbol. This is the Martinist definition:
Just as the head and tail are opposites existing as a whole, the serpent
swallowing its own tail demonstrates that eventually the tail would accept the
same qualities as the head. This means that the lower self and its associated desires will eventually be transformed through personal alchemy and become re-integrated with the head – or the higher self: the Master.
The ouroboros often symbolizes self-reflexivity or cyclicality, especially in the sense of something constantly re-creating itself, the eternal return, and other things such as the phoenix which operate in cycles that begin anew as soon as they end. It can also represent the idea of primordial unity related to something existing in or persisting from the beginning with such force or qualities it cannot be extinguished (WikiPedia, 2013).