For example if you have an european style one phase per room wiring, if you have a power failure on one phase, you could in theory use that cable to power the disabled part of your house.
Don't ever fucking do it tho. This is an incredibly, incomprehensibly retarded thing to do, and might kill someone, including repairman working to restore your power
I've used them in a pinch to run a circuit on a generator, but it can be really dangerous in several ways.
You flip the breaker off and plug the generator into one of the outlets on the circuit using one of these and it'll power the rest of the circuit.
But pretty often the generator will put out a lot more amps than the wire in the wall is designed for, and you've bypassed the breaker. If you hook up too many devices you can draw too much current for the wires and start a fire.