All EM waves transfer energy from a source to an observer. The source might be the Sun, a lamp or a radio transmitter. The observer is whatever absorbs the waves, such as your skin, your eye or an aerial. The waves carry energy across the gap between them without any matter travelling from the source to the observer.
Infrared radiation from the Sun transfers energy to your skin, which feels warm. Microwaves are absorbed by water molecules in food, so the water heats up and cooks the food. Visible light transfers energy to cells in the retina of your eye, which is how you see.
Radio waves from a transmitter make electrons in a receiving aerial oscillate, which produces an alternating current. Gamma rays carry a lot of energy and, when absorbed by living cells, can damage them.