The sounding of notes together. The notes may be together on the same Instrument, sung or played as a Chord, sounded on different instruments or voices (like Barber's Shop) or be the intentional coming together of two or more melodies (Counterpoint).
Harmony really relates to two (or more) Frequencies or Pitches being sounded simultaneously resulting in a 'harmonious' sound. The rules of harmony were worked out by Pythagoras although the effects were well known. Certain ratios of string length in stringed instruments or air column in wind instruments produce notes of a particular pitch. Combinations of notes of instruments with different length strings or air columns may sound pleasant or not (discordant).
Halving or doubling the length produces a note an Octave higher or lower respectively. As the notes are exact proportions of each other (1:2 or 2:1), the result sounds harmonious. Other simple proportions which sound harmonious are: 2:3 (a Perfect Fifth) 4:3 (a Perfect Fourth) 5:4 (a Major Third) and 6:5 (a Minor Third).
The first and second notes of a Scale sounded together is a discord or dissonant Interval. The first and seventh interval is also dissonant. The first and third (Major or Minor), first and fourth, first and fifth and first and sixth are pleasant intervals with different characteristics. Taking any note as the root note, this relationship holds true.