I think they mean order as in balance/neutrality, or in other words he represents the overseer preventing Yveltal's destruction or Zerneas' lifebringing upsetting the natural balance of the world.
He's like the Rayquaza to Xernas and Yveltal's Groudon and Kyogre. If they come into battle with each other, the natural ecosystem would be thrown out of whack. Yveltal will continuously drain the life from things. Xerneas would continuously grow things (which could cause overpopulation and reduce the supply for everyone). If such a thing happens, Zygarde would emerge from his cave and use his ability to suppress the powers of the one that went out of control. That way, the other can come in and fix the balance.
3DS FC: 2578-3118-6645 PSN: PowahBoxers I need to play Paper Mario: The Thousand Year Door again...