Radiation is the transfer of energy by electromagnetic waves. Radiation is a type of heat transfer that doesn't require other matter in order to transfer energy. The sun's energy travels millions of miles through empty space in the form of electromagnetic waves.
Radiant energy is given off by hot objects and directly absorbed by cooler objects.
A fire in a fireplace transforms the energy in the wood it's burning into electromagnetic energy. The electromagnetic energy from a fire radiates heat all around the room.