Multi-core power cables are useful any time you're carrying a circuit in and out of an appliance at the same location. Usually that's just 2 plus an optional ground. For electronic devices with specialized power requirements, there may be several power lines in the cable carrying different voltages. Single-core power cables are especially useful in high amperage appliances, such as welding equipment, and in DC automotive wiring in which the chassis serves as the ground. Thick cables for high amperage are hard enough to manage and wire without being bundled into a multi-core monster. It also makes sense to use single core cables with a ground chassis so that you only have to run one wire, and just complete the circuit to ground at the point of use. Single-core power cables can also be useful in serial or parallel wired appliances, or power supplies, such as a string of lights, or an array of batteries.
