Heat can be transferred in three ways: Radiation, Conduction and Convection. Conduction is heat transfer by two solids touching. Or when you put your hand on your heater, you feel your hand getting warmer. Convection is heat transfer to fluids (gases). That is why the air in your room heats up when you put a heater in it. Radiation is the weakest form of heat transfer, by far. But if you aren't surrounded by an atmosphere or ocean to dump heat into, and instead are surrounded by a vacuum, radiation is the only way to get rid of heat. Conductive transfer will constantly heat up the spacecraft until parts start to melt if you cannot radiate the heat fast enough. Hence the need for large radiators on spacecraft that produce a lot of heat, e.g. the ISS or even the shuttle, whose whole payload bay doors were used as radiators and needed to be opened somewhat quickly once in orbit or the shuttle would overheat.