Non-harmonic tones are simply melody notes that are not part of the chord in force at the moment. For example, if the chord is C7, the chord notes are C, E, G, and Bb. Any other note in the melody which is not one of those 4 notes is said to be non-harmonic — in other words, not a member of the C7 chord.

Sometimes non-harmonic tones can be quite dissonant; such as an F# in the melody while a C chord is in force. Usually the non-harmonic tone resolves to a chordal tone, hence resolving the dissonance into consonance. A good example of this is the 2nd note of the melody of “Maria” in West Side Story. There is a flat 5th juxtaposed against the tonic chord, but then resolved up 1/2 step to the 5th, creating a beautiful resolution.