A wave is a disturbance of a medium which transports energy through the medium without permanently transporting matter. In a wave, particles of the medium are temporarily displaced and then return to their original position. There are a variety of ways to categorize waves. One way to categorize waves is to say that there are longitudinal and transverse waves. In a transverse wave, particles of the medium are displaced in a direction perpendicular to the direction of energy transport. In a longitudinal wave, particles of the medium are displaced in a direction parallel to energy transport. The animation below depicts a longitudinal pulse in a medium.
The animation portrays a medium as a series of particles connected by springs. As one individual particle is disturbed, it transmits the disturbance to the next interconnected particle. This disturbance continues to be passed on to the next particle. The result is that energy is transported from one end of the medium to the other end of the medium without the actual transport of matter. In this type of wave - a longitudinal wave - the particles of the medium vibrate in a direction parallel to the direction of energy transport.
For more information on physical descriptions of waves, visit The Physics Classroom Tutorial. Detailed information is available there on the following topics:
The Nature of a Wave
Categories of Waves
Sound as a Longitudinal Wave