Everyone here has an important wish. Something they were willing to do everything for. Kill other teams, die themselves, overcome any obstacle. The Judges have the power to grant these wishes. But something you'd do anything for has to be earned. She didn't say why, but it's important to them that we all be here. In exchange for that, they grant our wishes.
So, what we, Ophiuchus, are for... we make sure they earn what they want more than anything. And by doing so, we earn our own greatest desire.