It is currently unknown how long they have been operating, but from what Kriem says the organization is larger than anyone believes. It is also unclear how powerful Ouroboros really is, but is hinted that its influence is enormous in scale.
Maverick made a deal with the organization to get a steady supply of villains for Hero TV, in exchange for the Brooks' technology. It would seem he has command over a small, yet large fraction of the organization, given he's manged to constantly supply criminals for Hero TV over the years. However, it's possible Ouroboros has some connections in the government that allow them to get their thugs out of jail for repeated use.
Unrelated to the Tiger & Bunny storyline, Ouroboros is an ancient symbol of a serpent eating its own tail, meant to represent self-reflexivity or cyclicality.
During the epilogue, a local kid, while buying Barnaby Brooks Jr. and Wild Tiger cards, drops his dollar in a puddle and the head is replaced by the Ouroboros symbol. This would imply they've infiltrated the ruling government of Sternbuild.