Waves with and without a medium
A water wave travels through water; a wave on a rope travels through the rope. The material a wave travels through is its medium.
Waves in a material medium
The particles of the medium do not travel with the wave. It is their motion, passed from one particle to the next, that carries the energy through the medium as a wave. Many other materials carry waves in the same way.
We hear sounds because sound waves travel through the air. Sound travels through liquids and solids too, not only through air.
Waves with no material medium
Some waves need no material medium at all. Light is one. The space between the sun and the earth has no air in it, yet light and heat reach us from the sun. They travel as electromagnetic waves, which need no medium.
Radio waves are electromagnetic waves too. Programmes broadcast from a radio station reach the radio in your home through the air, but the radio waves do not need the air to get there.
Need a material medium
Water waves, waves on a rope, sound waves.
Need no medium
Light, heat from the sun, radio waves — all electromagnetic.