Leakage current is the current that flows out in the circuit and doesn't come back. This comes from poor insulation between earth and live conductors. There will of course always be some leakage current, since no material is a perfect insulator.
It's typically a concern when it comes to wiring protected by an RCD (GFCI), since it is designed to trip if the incoming and outgoing currents doesn't add up. A PC will leak about a 1mA and the recommended maximum level on a European RCD is 10mA, as it's designed to trip between 15 and 30mA. This means that you can only have about 10 computers on one RCD.
