The Collapse was a mysterious event that occurred on August 8th 2209, causing widespread chaos across Stark. According to Charlie and Emma, it happened just after April Ryan disappeared from Newport, so it is very likely the Collapse was at least concurrent with, if not a result of, Gordon Halloway's ascension to the Guardian's throne and presumed re-establishment of the Balance.
Just what the Collapse entailed has never been fully explained. In Dreamfall's manual, it is simply described as "something that happened", though as Zoë Castillo describes how her father kept her indoors during the Collapse, it is likely that there were changes to the sky. After the Collapse, humanity could no longer 'fly without wings', communicate with the other side of the planet, or even make contact with Earth's space stations or colonies.
Charlie and Emma mention seeing strange things during the Collapse. When talking about the fate of April with Zoë at the Fringe Cafe, Charlie says "I didn't believe her. I'm still not sure I do, despite the things I saw during the Collapse." Emma later says "Most people don't remember. Or they pretend to have forgotten. Those of us who saw it... You don't forget something like that."
From the official site:
Ten years ago, something happened…
No one can remember exactly what happened, or why, but it changed the world. Completely.
After almost two centuries of complete freedom, we were trapped, earthbound, the skies above us closed, cities on the other side of our planet inaccessible. For a time, we were powerless, frozen, shocked into silence by events that we couldn't explain or understand...
...and then, slowly but surely, we picked up the pieces and moved on. A week, maybe two, and civilisation brushed off the dust of the past and set its sight on the future. So we couldn't fly without wings anymore. So we couldn't communicate with those who had moved beyond our space. After all, we had lived like this before, and we could do so again.
Moving at impossible speeds close to the ocean surface, the hydrofoil connected us again with our relatives on the other side of the Earth. Before Vactrax tunnels snaked their way to every major city, the hydrofoils were indispensable. And they are still in use, particularly across the Atlantic and Pacific Oceans - connecting major cities like, for example, Newport and WATI City.
Ten years on, humanity has learned to live in a changed world, and while the memory of the Collapse lingers, it's not something we dwell on. So we don't quite know what happened, and we can't really recall the details of those dark days, but life goes on, we have regained our freedom, our wings, and the future is as bright as it ever was.