What is in it
A major 7 is a major triad (root, major 3rd, perfect 5th) with a major 7th added above. From C that is C, E, G, B. The triad is the same bright, stable chord you already know; the new note is the B, sitting one half step below the C an octave up. That tight gap between the 7th and the root is the sound of the chord.
On the staff
Bright, but hanging
The major 7 keeps the brightness of the major triad and adds a quiet unrest. Its 7th rubs gently against the root a half step away, which is a dissonance, but a soft one that the ear does not feel a strong need to resolve. The chord sounds finished and unfinished at once: stable enough to rest on, coloured enough that it never quite closes. That hanging quality is why it became the signature sound of cool jazz and quiet soul rather than the bare major triad. In jazz it is the home chord of two of the major scale's modes: Mark Levine pairs the major 7th with the Ionian scale when it works as the I chord and with the Lydian, raised 4th and all, when it works as the IV.
Major 7 against dominant 7
These two chords share a major triad and differ only in the 7th, so they are the pair most worth telling apart by ear. The dominant 7 has a minor 7th and a tritone inside it, so it sounds restless and wants to move. The major 7 has a major 7th, no tritone, and simply floats. If a bright four-note chord pulls toward a resolution, it is dominant; if it hangs in the air, it is major 7.
How Aubel handles it
Major 7 unlocks sixth, right after the dominant 7. The pairing is deliberate: both sit on the same major triad, so the only question your ear has to answer is whether the 7th is minor or major. The cue is the half step between the 7th and the octave, and the absence of the dominant chord's pull. Minor 7 unlocks next, which moves the whole thing onto a minor triad.