Checking Receptacles In Home, What Does Open Ground Mean On My Testers?

I think it means that somewhere down the line the grounds no longer reach the electrical panel. The tester checks for continuity(continuous path) back to the electrical panel. So when it says open it means the path does not go all the way to the panel from the plug tester you can run the proper size ground all the say to the panel or take apart all of the devices until you find a box where the grounds are separated. If there was a recent remodel, maybe the path was cut by the contractor?

It means that the circuit breaker panel or fuse panel in your home is not grounded to the power meter outside your home. Possible options are to obtain copper wire and ground it yourself, or call an electrician.