The Ouroboros or Uroborus dates back to ancient times, and is depicting a dragon or serpent eating it's own tail. It often represents constant re-birth from destruction, or an infinity. Interestingly, it has been seen in alchemical illustrations, where it represents a circular nature of the alchemist's opus.
 In the Anime
The Ouroboros appears on the Homunculi in various locations. It's symbolic of their immortality and the way that a Homunculus is created. It seems to have certain effects on the Homunculus in the anime as well. For instance Gluttony looses his ability to think rationally once his is triggered alchemically - reducing him to an animal like state.