Here's the breakdown:

* Longitudinal Waves: The particles in the medium vibrate parallel to the direction the wave travels. Think of a spring being compressed and expanded, the motion is back and forth along the spring's length. Sound waves are a great example of longitudinal waves.

* Transverse Waves: The particles in the medium vibrate perpendicular to the direction the wave travels. Imagine shaking a rope up and down, the wave moves horizontally, but the rope's movement is vertical. Light waves and water waves are examples of transverse waves.

Let me know if you'd like more details on either type of wave!