Where is "Back up my data" stored? Can it be edited?
There isn't any way to get to it. It is basically turning on and off a developer facing backup feature. Each app can write what it wants to into a certain amount of space, and Google takes care of sending it back to the app when it is reinstalled.

Even if you were to write an app for it, you'd only be able to access the storage linked to that developer key, not the other apps that use the service.

For more info on what that option does, see my answer here.