Why are there two layers of dry wall in my ceiling, and how can I patch it?
We've done a double layer of drywall to slow the spread of fire in multi-unit developments, specifically between the ceiling and attic space. However, judging by the gap, I'm guessing that you might have this done as a retrofit to block sound. There will be somewhere that the drywall is attached, and it's likely going to be metal tracks running every 16". Normally, we'd attach the tracks directly to the joists, but if this is was a decision made after the home was built, they may have elected to go over the drywall instead of making a mess removing the existing drywall.

If you want to patch the drywall, you can either install additional blocking between the drywall at this opening to give you something to screw into, or you can cut back the drywall to the current tracks and attach your patch there.

Edit: If you decide to use blocking between the drywall, some thin wood would be be easy to install, and you're not getting a lot of sound protection at this spot anyway. You'll want a piece of wood behind each sheet of drywall, and then screw through the drywall/wood/drywall/wood to give you a solid edge to work with. You can get longer drywall screws that can make it through the entire assembly in one shot. If you go with the long screws, I'd recommend using a clamp to hold it tight.