Be very careful dealing with mains voltage. It can kill you, your Tessel, your computer, burn down your house, etc. If you want a simpler and safer solution for switching an outlet on and off, check out https://www.adafruit.com/products/268, which you can control from a Tessel GPIO pin.
A relay is just an electrically-controlled switch. Each relay module channel has two pins. When the relay is off, they are not connected to each other, and electricity can't flow. When the relay is on, the two pins are connected to each other by the relay, completing the circuit and allowing electricity to flow.
If you've connected both wires going to the PS3 to the pins of the relay module, nothing is supplying power. Relays only switch on and off an existing supply of power; they don't supply power on their own. The relay goes in series with the positive (DC) or hot (AC) wire between the supply and the load, and the negative (DC) or neutral (AC) line is connected straight through to the supply:
The relay acts like switch S1 in the schematic above. When it connects the battery to the LED, the LED lights up.
I'd recommend trying this with something battery powered or powered from your Tessel first. Don't mess with mains power until you know what you're doing.