In acoustics the term "harmonic" is a noun used to describe an overtone or partial whose frequency is an integer multiple of the fundamental frequency.  
The diagram illustrates a fundamental frequency and the first five harmonics with frequency ratios of 2:1, 3:1, 4:1, 5:1 and 6:1 in relation to the fundamental frequency.
harmonic series equal tempered tuning
In music the term is an adjective which refers to the system of harmony and distinctions between consonance and dissonance. 

There are interesting historical relationships between the musical and acoustical meanings of these words stemming from the ideas of Pythagorous and his discovery of the properties of the harmonic series and the relationship of sound, music, number, and nature.