* Transverse waves have oscillations that are perpendicular to the direction the wave travels. Imagine a rope tied to a wall. If you shake the rope up and down, the wave that travels down the rope is transverse. The wave moves horizontally, but the rope itself moves vertically.

* Longitudinal waves have oscillations that are parallel to the direction the wave travels. Sound waves are a good example. The air molecules vibrate back and forth in the same direction that the sound travels.

When you wave your hand, the movement of your hand (the disturbance) is perpendicular to the direction the wave travels (from your hand out into the air). Therefore, it's a transverse wave.