This question is in need of an updated answer, after the airing of Series 9 last year.
In the two-parter story comprising episodes 7 and 8, "The Zygon Invasion" and "The Zygon Inversion", we learn that the treaty drawn up by the humans and Zygons involved
twenty million Zygons rehabilitated on Earth, taking the form of humans and living unobtrusively among us. The twin Osgoods, one human and one Zygon, were the maintainers and symbols of the peace, which was also ensured by the Osgood Boxes, one red and one blue.
This much we know at the very start of "The Zygon Invasion", from the message recorded by the two Osgoods at the time the treaty was made:
OSGOOD 1: Operation Double is a covert operation, outside of normal UNIT strictures, to resettle and rehouse an alien race in secrecy on planet Earth.
OSGOOD 2: With UNIT's help, twenty million Zygons have been allowed to take human form, been dispersed around the world, and are now living amongst us.
OSGOOD 1: We're making this in case something goes wrong. In case UNIT is infiltrated. In case something occurs to unmask the Zygons.
When the peace breaks down and the Doctor is called back (the "Nightmare Scenario"), we also learn what the Osgood boxes do:
there are two buttons in each box. Supposedly, one of these buttons would save, and the other would destroy, each of the humans and Zygons. But it transpires at the very end of the episode, after the Doctor does his awesome speech, that in fact both boxes are empty, and the point of the whole thing is to make both sides understand what war is all about and that what they should really do is "Sit! Down! And talk!"
As the Doctor explains:
DOCTOR: One of those buttons will destroy the Zygons, release the imbecile's gas. The other one detonates the nuclear warhead under the Black Archive. It'll destroy everyone in London. Bonnie. Bonnie, sweetheart! One of those buttons will unmask every Zygon in the world. The other one cancels their ability to change form. It'll make them human beings for ever. There are safeguards beyond safeguards. I did this on a very important day for me and this ceasefire will stand.