Mechanical Waves
A wave is the term used for movement caused at a fixed point, whereas the medium will ripple from the point of agitation to its end. The particles in the medium affected by the wave move in a particular direction based on the type of wave, returning to their original positions once the cause of the agitation no longer exists.
Transverse Waves
The particles in transverse waves move perpendicular from the base or point where the medium is agitated. If it were possible to visually fix onto a particle of the medium, the particle will not move with the wave's motion. Rather, its movement will remain consistent, up and down. Imagine a glass elevator filled with water, moving up and down quickly, in a pulsating fashion. The waves created by this movement are transverse waves.
Longitudinal Waves
The particles of longitudinal waves move parallel to the point where the wave is created, and like transverse waves, the particles in a longitudinal wave do not move with the wave.
Imagine a square pool of water with moveable borders. If one border moves slightly back and forth so that it is inside the pool and then back to the border, it will cause longitudinal waves along the pool's surface. If it were possible to fixate on one particle within the pool, the particle would move back and forth, just as the wall's border moves, and once the agitation ends, the particle will remain in its position; it does not follow the movement of the wave.
Ocean Waves
Ocean waves have both transverse and longitudinal waves that cause the particles to move in clockwise circles from left to right. These circles are perpendicular to the base of the water. Imagine a surfer on a beach, riding a large wave. The top of the wave curves forward and crashes in a circular movement, if viewed from the side. This is evidence of both transverse and longitudinal waves, and their movement is more obvious in shallower water.