The sky is cold, the Earth is warm, and the Sun is hot. If you have heat you want to get rid of (and in a spacecraft you usually do, since vacuum is a great insulator), you put it into a panel with good heat radiation characteristics and point it at the sky, and arrange shades so it can't see the Earth and (especially) the Sun.

The panel then being hotter than the sky, it sheds heat off into the universe, cooling itself, and the spacecraft.

This is why you will usually see solar panels and radiator panels perpendicular to each other. The solar panels want to see the sun, the radiators don't.

Thermal radiation is an order of magnitude less efficient than other forms of heat transfer, but it gets the job done. It helps that you're radiating to the dead of space, which is near absolute zero (efficiency is dependent on the black-body temperature of what you're radiating "to").

That's the why the radiators have to be so huge, and are kept out of direct sunlight.