Waves transport energy without anything material actually moving.
If you have been at a sports event or other performance with a large
audience you may have been part of a wave yourself. The wave
where people rise and sit back down in a coordinated way so as to
create a traveling wave. The important lesson to take home from
this example is that a wave can propagate with nothing
material propagating with the wave.
This type of propagation is as real as the
motion of a particle. It transports energy and it transports
information. This type of wave is called a transverse wave because
the local motion (vertical) is perpendicular to the (horizontal)
motion of the wave itself.
The speed of the wave is determined by local characteristics
of the ``medium'' in that case the audience.
We can estimate the speed of this wave by considering what happens
locally as the wave passes by a particular persons seat. We estimate that a person begins to rise when he sees a person N seats up
standing tall. Say that it takes a time 
to rise and sit back down again then the person we are considering will be standing tall
a time 
after he started rising. In that time the crest of the wave has thus propagated by the distance Nd, where d is
the average distance between members of the audience in the direction of the wave. The phase velocity of the wave is thus
Putting in numbers we estimate
