Mutually Insulated Circuit
So the idea is (depending on the spec) that two portions of the circuit or cable should be isolated. Take for example an AC power supply that is rated for a 3kV isolation, if the DC side and AC side are isolated (with an isolation transformer) then you could safely connect a 3kV source on one part of the supply and current should not flow to the other (unless there was a dielectric breakdown at the transformer). This test would also ensure that the creepage and clearance on the PCB is doing it's job. The current is measured on other conductors to see how much bleeding from one insulated portion of the circuit to the next. Another thing that is usually tested on most products is leakage current from the Line or Neutral to ground. A product could shock someone if the ground wasn't connected.

Some manufacturers\specs require cables to be tested so the insulation strength can be tested, so you would test the cable connected to a hi-pot tester and test the parts of the circuit that are 'mutually insulated' or the sections of the cable that touch. This would depend on the structure of the cable and connector. 

I can't say by your diagram which circuits are mutually insulated and I don't know if you need a cable test or a power supply test, by the standards you are required to test to. Work with the regulatory entity that your product needs to pass to find out what kind of testing needs to occur.