Why a Relay?
Relays are an important component in wiring fog or driving lights with a Hi Amperage (20A+) draw. Basically, the relay protects the switch from getting hot and creating unwanted resistance to existing wiring. Resistance equals heat and excess energy use. When the light is switched "on", the low current change is detected by the relay and simple "toggles" the relay ciruit to make the higher current connection to the fog lights.
In other words, the relays function is to detect the current change (lights on) and send the electricity to the lamps or other device via its own electrical line circuit.
There are many examples and explanations / howto's on the internet, but this one from Moss Motoring is nicely done and well ordered.
Moss Motors LTD All Thing British