When a string that is fixed at the ends is made to vibrate, a standing wave is formed in which certain points on the wave (nodes) do not move, and other points (antinodes) undergo maximum displacement.

The lowest frequency of a standing wave (also called the first harmonic) has a wavelength that is twice as long as the string, since each there are only two nodes (each end) and a whole wave must have three nodes.

The next highest frequency the string can produce is called the second harmonic. The first harmonic will have a wavelength equal to the length of the string (3 nodes = one wave)

Each successive harmonic is made by shortening the wavelength enough to produce one more node. Since each end is fixed, it must be a node. This limits the wavelengths of the harmonics to those which will fit between the ends of the string and end at nodes. Any other waves would cancel out.

When a string is plucked, it mostly produces waves of the first harmonic (fundamental frequency)

But it also produces waves of the 2^nd, 3^rd, 4^th, etc. Harmonics as well. These waves all combine to form a complex waveform. The pitch of a guitar string is the first harmonic, and the timbre

(sound quality) of the note is made by the other harmonics. The higher harmonics are also called overtones.