Wave motion takes place all throughout nature, from the waves of the ocean to the electromagnetic waves that comprise visible light. Though different types of waves involve different materials, they can be described according to some key characteristics that they all share.
Mechanical waves (as opposed to light waves) transfer energy within a medium. The wave itself is not a single object or mass, but expresses a transfer of energy or vibration from one point to another. A good example is a wave on a string-individual pieces of the string only move up and down, while the wave transfers energy from one end to another. This characteristic is common to all waves: individual particles in a medium oscillate around an equilibrium point, while the wave itself translates over a distance at a certain velocity.
It is easy to visualize and draw a wave that moves horizontally while the particles in its medium move vertically-this is called a transverse wave. You can make this type of wave by shaking a string or spring up and down. In this case, particles in the material have an upward velocity as the wave approaches, followed by a downward velocity as it passes. The wave itself has its own velocity in a horizontal direction, as you can see when you whip a rope and watch the pulse travel down to the end. Thus, the material oscillates in a direction perpendicular to the wave motion.