Here's why:
* Transverse waves: The particles of the medium oscillate perpendicular to the direction the wave travels. Think of a wave on a string or the ripples on a pond. The string moves up and down, while the wave travels horizontally.
* Longitudinal waves: The particles of the medium oscillate parallel to the direction the wave travels. A sound wave is a good example. The air molecules compress and expand in the same direction the sound wave is moving.
Let me know if you'd like more examples or explanations!