Harmony can be thought of as the notes that support and add character to a melody. The basic building blocks of harmony are chords. A chord is a group of notes played simultaneously (e.g., strumming on a guitar). There are many different types of chords which have different names and sounds. If you look at sheet music you will see chord symbols written above the melody. These symbols will be things like C, Cm, Bb7, E7#9 etc.
All of these symbols describe chords which have different types of sounds. Chords are usually played in a repeating sequence called a chord progression. A chord progression works a bit like a basic drum beat, except that the sequence may repeat every 2, 4, 8, or 12 bars instead of every one or two bars.
Once again, the best way to learn about chords is to learn a bit of basic guitar or keyboard. In the final examples written here, the guitar plays a chord progression and the bass plays a melody (bassline). All the parts combine to give a strong sense of rhythm. Put these parts together and you have the three basic elements of music, rhythm, melody and harmony.