The easiest way to understand this is through a diagram...
If you're still confused:
- Imagine holding a rope between you and a friend (or a teacher if you have no friends)
- Shake the rope up and down to create a transverse wave
- Kinetic energy is sent through the wave to your friend, you know this because your friend will feel the kinetic energy.
- But the matter (the Rope) hasn't moved, because if it had your friend would end up with a big pile of rope in their arms, and you'd be standing there with your hands empty looking rather stupid.... @_@