The Ouroboros is an ancient symbol depicting a serpent or dragon eating its own tail. It is a symbol of a constant cycle of death and rebirth, much like a werewolf's transformations destroy their bodies and then rebirth them in their wolf form and then back into their human form. In the show 'Ouroboros' represents the Order of the Dragon. Project Ouroboros is kept within a large metal and glass box with small viewing windows on the side, from which a mysterious bright light is emitted.
Dr. Pryce shows Roman Project Ouroboros after he arrives at the Institute, before injecting him with a liquid causing Roman to fall into a coma. Towards the end of season one, the inside of the mysterious box is shown to contain a humanoid in a placenta-like environment.
The Ouroboros is also similar to the myth of the Jormandungir, a millennium year old story of a serpent cast into the ocean by gods, then growing around the entire earth, to the point where it was biting its own tail. These creatures where meant to foretell the end of days, as it would become like a constrictor snake that crushed all like on earth into nothing.