on Gas fuel injected vehicles it kills the ignition circut ( coil) and the engine management which shut off the injectors and fuel pump. On carb vwhicles it simply shuts off the ignition, on occasion there is also a fuel cut solinoid on the carb.
On older mechanical pump diesels there is a solinoid that is energized that shuts fuel off to the engine. some even older mechanical pumps have a valve that is actuated to cut the fuel and has no electrical source. ( this would be a knob on the dash that you pull or push)
things get real exciting when diesels are able to pull oil or other fuel source independant of the injection pump/injectors.
usually results in a small yard sale under the vehicle, or at least in the oil pan.