What is harmony in music?

Harmony is two or more notes played together at the same time. As soon as there is more than one pitch sounding at a time, you have harmony. Even if nobody is actually playing chords, or even if the notes are part of independent contrapuntal lines, you can hear the relationship of any notes that happen at the same time, and it is this relationship that makes the harmony.
But the concept of harmony in music theory generally refers to building chords, chord qualities, and chord progressions.
Harmony strictly applies to pitched instruments, so clapping and stomping at the same time won’t create a harmony.
You might associate harmonies with vocals, but they can be produced on all multi-pitched instruments – guitars, synths, pianos – or a combination of single-pitched instruments playing different notes at the same time, like two people singing together.
From chart-topping R&B songs to folky acoustic tracks to orchestral works, harmony is a central element of just about everything.