A major chord (or a "major triad") is a chord composed of three notes, where the distance between the first and the second note is four semitones and the distance between the second note and the third note is three semitones.
The C major chord, for example, consists of the notes C, E, and G. There are four semitones between C and E. There are three semitones between E and G.
The major chord can also be described as composed of the major third and the perfect fifth of some scale. In the major scale in C, for example, the third note is E. E is a major third, because the interval between the first note C and E is four semitones. The fifth note on the scale is G. It is a perfect fifth, as the interval between the first note C and G is seven semitones.
Examples of scales with major chords
The following are examples of where the major chord occurs in common heptatonic scales.
Examples of relationships between the major chord and other three note chords
Shifting the second note of the major chord one semitone down produces a minor chord (i.e., switching from a major third to a minor third).
Shifting the third note of the major chord one semitone up produces an augmented chord (i.e., switching from a perfect fifth to an augmented fifth).
Shifting the second note of the major chord one semitones up or two semitones down produces a suspended chord (i.e., switching from a major third to an augmented third or a diminished third).