A wave is a disturbance that travels through a medium, such as water, air or a solid. The source of the wave makes the particles of the medium vibrate, and those particles pass the disturbance on to their neighbours.
The important point is what moves and what does not. Waves transfer energy from one place to another. They can also carry information: sound carries speech and music, radio waves carry television and phone signals, and light pulses carry data along optical fibres.
Waves do not transfer matter. The particles of the medium only vibrate about a fixed position and then return to where they started. The wave moves on, but the medium stays in place.