Sound is the phenomenon of a wave moving through a medium. This is differentiated from light or radio waves in that the waves move through a material medium, rather than the electromagnetic spectrum. Sound waves are usually produced by an object vibrating (such as a rubber band held taught and plucked), or by two or more objects having friction (such as tapping on a chair arm or rubbing one's hands together.) Although sound waves usually travel through air and are heard by the ear, they can also travel through liquids and solids and can be felt 1.
Sound has several characteristics used to describe it. Volume (amplitude) refers to the loudness or intensity of sound. A larger sound wave means a louder sound. Pitch (frequency) refers to how high or low a sound is. A shorter wavelength has a higher pitch and is perceived as having a greater volume, while longer wavelengths have a lower sound. Timbre has to do with the tonal quality of sound. A bird chirping and thunder have very different tones, as do an "eeee" sound and an "oooo" sound. Resonance is the way a sound reflects off a surface. A harder, smoother surface reflects more sound, creating an echo.
What accounts for the rich variety of sound is the infinite ways a wave can be structured. Sound waves are often represented using a sine wave on a graph, but the wave it represents is much more animated. A good way to picture this is by looking at water waves. The wave theory of sound was developed in this same way, by observing water.