Things that are harmonious go together nicely, like notes in music or people that work well as a team.
The idea of things being harmonious comes from music — when certain notes sound good together, they are harmonious. But this concept applies to many other things and people, too. You could say pieces of art that look good next to each other are harmonious. A basketball team that shares the ball and gets along well is harmonious. Anytime people get along, they're being harmonious. In a totally harmonious society, there would be no war or hate.