The short answer is that a harmony line is a second melody that   accompanies the primary melody.

Harmonies are related to chord progressions, but they are different because they are single note lines that have similar characteristics to the melody.   They are different from counterpoint, because they accompany the melody, rather than move in contrast to it. The effect that a harmonic line has is to provide interest by defining the chords that are implied in the melody. In musical analyis, the melody is often called the salient line, and the harmony is called the recessive line--