When you pluck a string, a very interesting thing happens…
Not only does the string vibrate like this…
but it also vibrates like this…
and like this…
and like this…
and this…
and so on and so on.
Notice that the “shape” of each vibration is found by dividing the length of the string into smaller equal-length sections that are each whole number division of the total length of the string: 1, 1/2, 1/3, 1/4, 1/5 and so on.
The first vibration is called the fundamental and is perceived by our brains as the pitch of the note.
The “extra” vibrations are called overtones or harmonics.
These overtones are typically of a smaller amplitude, and therefore are not as loud as the fundamental. They add harmonic “colors” to the fundamental pitch, which we perceive as something called Timbre.