Harmonics are the frequencies (or 'pitches') that combine together to give tone colour to a note. Every instrument has a distinct timbre caused by the harmonic content of its sounds. This depends on the size and shape of the instrument and the method by which the note is produced e.g. blowing or bowing.

Question: How can we tell that this is a violin and this is a trumpet?
Answer: Because their timbres are different.