As seen in the diagrams above and below, the individual particles in the medium oscillate (move back and forth) about their equilibrium position (original resting position). They are only temporarily displaced and always return to their original equilibrium positions (keep your eye on the orange particles). - ie., they do not travel with the wave - there is no movement of matter.
Click to see the animation!
There is, however, a movement of energy. As particles interact with neighboring particles, they transfer their energy to them. The neighboring particles in turn then transfer this energy to their neighbors, and so forth down the line.
In conclusion, a wave can be described as a disturbance that travels through a medium, transporting energy from one location to another location without transporting matter.