Harmonizing

It's a way of producing harmony.

When two (or more) different notes are played or sung at the same time, the notes combine with each other to produce a quality of sound distinct from the sounds of the individual notes, i.e they harmonize with each other. Even when you play a simple chord, the individual notes harmonize with each other to produce a harmonic effect unique to that chord type.

If you take a melody and sing or play another melody at the same time, the notes of both melodies will combine to produce this effect, The art of harmonizing involves skilfully combining notes in such a way to produce the desired harmony.

Two melodies do create a harmony, but when people talk about 'harmonizing' you have to consider the source.

When guitarists talk about 'harmonizing', they usually mean playing a melody in intervals. If Guitar I plays CDEFGABC, Guitar II might play EFGABCDE - that second guitar isn't playing in Phrygian mode, it's creating thirds against the first guitar.

The type of third you get depends on the position in the scale, because the scale itself isn't symmetrical - the half steps aren't evenly placed. That's true of harmonizing in any interval except octaves.

So in my scale example, you'd get:

CE = major third
DF = minor third
EG = minor
FA = major
GB = major
AC = minor
BD = minor
CE = major

Harmony is a big concept, and there are lots of ways to have two instruments playing different notes. The simplest is for one voice to stay on just one note (a 'drone') while the other does a melody - it'll create intervals when the second voice moves. The most complex is what Fretsource describes: two independent melodies. The 'main' melody is the 'cantus firmus'; the other one is the 'cantus punctus', from which we get the name of that style of harmony - counterpoint.