A major seventh is the chord you get when you take a major triad and add to it the seventh note of the major scale. They're notated Cmaj7, or sometimes (in jazz) with a small triangle: CΔ7.

For example, a G major triad is G B D. The seventh note of the G major scale is F#, so the Gmaj7 chord consists of G B D F#.

The major seventh isn't a strong cadential chord, and adds interest but little movement to a chord progression; it frequently appears as the I in the ii-V-I progression - Gm7 C7 Fmaj7 for example.

Compare with the minor seventh, dominant seventh and minor major seventh chords.