How do I fix a sinkhole in my backyard?
How old is the house?  If it's fairly recent, do you have any idea of what the property was like before being built on?  It's possible that the builder put down a lot of fill, and there was a large amount of organic material in that fill, or that he just dumped fill on top of what was there - stumps, trees, etc.  Depending on the composition of the fill used, you might be able to get away with just dumping earth or sand into the hole, but it sounds like a large area - which means that digging it up, removing the rotting organic material, and replacing it with fresh fill is really the only way to permanently fix it.

You might want to get a local plumber to come out and "scope" the hole to see if you can tell whether or not this really is your problem.