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.