Here's a breakdown:
* Longitudinal waves: The particles in the medium oscillate back and forth in the same direction that the wave travels. Think of a slinky stretched out and then pushed. The compression and rarefactions (stretches) move along the slinky, and the individual coils of the slinky move back and forth in the same direction.
* Transverse waves: The particles in the medium oscillate perpendicular to the direction the wave travels. Think of a rope tied to a post. If you shake the rope up and down, the wave will travel along the rope, but the individual sections of the rope move up and down.
Examples of Longitudinal Waves:
* Sound waves
* Seismic P-waves (primary waves)
Examples of Transverse Waves:
* Light waves
* Seismic S-waves (secondary waves)
* Waves on a string