Around here the on call-GP is the guy you go to when you need a GP in the weekends or evenings that absolutely can't wait until Monday or the morning, but that doesn't warrant an ER trip. For example if you have not-too-severe pneunomia - you need antibiotics, but don't have to be hooked up on oxygen.
If I call my GP after hours I get a tape that says basically "Wait until working hours or, in case of an emergency, press 1 and be connected to the on call GP".

The on call-GP 'position' is filled by different GPs that work in shifts. There is not one guy who is always the on call-GP: regular GPs have a on call shift every once in a while.

I don't know if it's the same where you're from.