Disclaimer! The instruments I use as examples do not create perfect versions of the sound waves I am trying to describe. These waves, like sine waves, do not exist in nature. They do however emit very close approximations of the sound waves in question.

Timbre is the quality of a soundwave that distinguishes it from other sounds. Timbre is based on many things. The first is the shape of the waveform. For example, something emitting a sawtooth wave (violin) will sound different than something emitting a square wave (saxaphone).

The next thing that will effect the timbre of a sound is the sound's envelope. Sounds with a fast attack and almost no sustain (snare drum) will sound different than sounds with a slow attack and long sustain (gong).

The shape and materials the instrument is made from give the sound waves it emits certain formants that carry through in the sound, no matter what it is playing. A wooden flute will sound different than one composed of metal. A french horn and a trumpet are made from the same materials, but have different shapes. They sound completely different.

Other componants of timbre are the way in which a sound is emitted (a whisper vs. a scream), the environmental space the sound is emitted in (outdoors in the park as opposed to a small empty room), and the state of mind of the observer (stoned vs. sober vs. irate vs. enthralled). I included the latter example because sound exists only in it's perception. Sound waves may exist if no one is around to hear them, but the timbre of a sound is completely dependant on an observer.