It is an ATX power supply - they operate by getting a "signal" from the motherboard that they should power on. What happens here is that two wires on the ATX connector get shorted momentarily.
You need to do this to turn on an ATX PSU without a motherboard:
Look at the main ATX connector. There's lots of different colored wires, but only one green one. Use a wire, or a paperclip which I use cause there's usually one handy, and connect the green connector to any black one. (Be sure to get the right connectors; shorting something to the wrong wire might cause serious problems). This will turn on the power supply. You can just use the main switch on the back of the thing to shut it off. Just don't leave it running too long without a big load on it. I'm not sure if it's true anymore, but I do have memory of reading something about running switching power supplies unloaded, and that it can be bad for them.