Waves transfer energy from one place to another without moving the material they travel through. There are two types. In a transverse wave the oscillations are at right angles to the direction in which the wave transfers energy. The ripples on a water surface are an example of a transverse wave.
In a longitudinal wave the oscillations are parallel to the direction of energy transfer. A longitudinal wave has regions where the particles are pushed together, called compressions, and regions where they are spread apart, called rarefactions. Sound waves travelling through air are longitudinal.
It is the wave that travels, not the water or the air itself. A cork floating on ripples only bobs up and down on the spot while the ripples move past it. In the same way, the particles of air vibrate back and forth about fixed positions as a sound wave passes. Someone across a room can hear a loudspeaker, but there is no wind carrying air from the loudspeaker to them.