Three types of mechanical waves are transverse waves, longitudinal waves and surface waves. Mechanical waves are different from electromagnetic waves in that they can't propagate in a vacuum; they need a physical medium, such as water or air.
Transverse waves are waves in which particles move perpendicular to the direction the wave is traveling. An example of this is a stretched slinky shaken to move up and down.
Longitudinal waves are waves in which particles move parallel to the direction the wave is traveling. A sound wave is an example of a longitudinal wave.
In a surface wave, particles on the surface of a medium move in a circular motion. For example, an ocean wave at the surface.