Three-note chords, or Triads, are the most common chords. Most generally they are composed of two thirds stacked on top of one another. Modifications of those stacked thirds produce different types of triads.
Major triads are composed of a root note, a second note a Major 3rd above the root node, and a third note a minor 3rd above that second note. A Major 3rd is 4 semitones above the root, and adding a minor 3rd means adding another 3 semitones. In total we have moved up 7 semitones from the root, the interval of 7 semitones is called a Perfect 5th. Therefore, looking from the root node, a major triad consist of a Major 3rd and a Perfect 5th.
Minor triads are composed of a minor 3rd interval and a Major 3rd interval stacked on top. The stacked thirds are reversed compared to the Major triad. That means they consist of a root, aminor 3rd and a Perfect 5th. While it's only a one-semitone difference with the second note flattened in comparison to the Major chord, it changes the mood of the chord. It goes from happy sounding (Major) to sad sounding (minor).
Augmented triads are Major triads with a sharp 5th. That means they are built from two Major thirds stacked on top of one another and contain the notes: root, Major 3rd, Augmented 5th. Augmented chords are rarely played as they have a dissonance to their sound, but can add an interesting touch when used right. The augmented triad chord formula is: 1 3 #5.
Diminished triads are minor triads with a flat 5th (tritone). They are composed of two minor thirds stacked on top of one another, which means they consist of a root, a minor 3rd and a Diminished 5th (Tritone).