One note played at a time is termed a unison; two notes together form an interval; three or more notes form a chord.
Chords are at the very crux of music theory -- or music alone, for that matter. Chords are three or more notes (or pitch classes; strictly speaking, notes are the written form of pitches) played together. But these notes don't necessarily have to be played simultaneously. Broken chords, or arpeggios, are three or more notes that aren't played at the same time but closely enough to be heard as a group or whole. And even the three-note rule is open to exception. Power chords, frequently used in rock music, consist of only two notes, but they still function as chords because they work, diatonically, in the same way that a major or minor chord would.
Chords are most often named based on their number of notes or the type of intervals involved. Chords classified by note number are given names such as trichord (three notes), tetrachord (five notes), and hexachord (six notes). Chords classified by interval are given names such as tertian (third chords), secundal (second chords), and quartal (fourth chords). Sometimes chords are named based on both qualities. Tertian trichords, for example, are chords with three notes, each a third above each other. These type of chords are actually the most common in western music, found frequently in rock and pop.
These chords aren't the only chords possible, however. There are several specialized chord types that seem to defy strict categorization. Inverted chords are created by adding a bass note that is not the root note. Seventh chords can be made by adding a fourth to a triad -- a third above the chord's fifth -- which makes the highest note a seventh from the root. Extended chords are those with notes that extend above a seventh, such as a ninth or an eleventh. But it's important to mention that no extended chord can go above a thirteenth. By that point, the notes included will have already been played somewhere in the chord, taking it back down to an eleventh or thirteenth.
