What is in it
A major triad is three notes: the root, a major 3rd above it, and a perfect 5th above the root. From C that gives C, E, G. The structure is two thirds stacked, but not the same size. The lower one, C to E, is a major 3rd of four semitones. The upper one, E to G, is a minor 3rd of three. Major third on the bottom, minor third on top. Reverse that order and you have a minor chord instead.
The outer interval, root to 5th, comes out to a perfect 5th in both major and minor. That shared 5th is why the two chords sound related rather than foreign, and why the 3rd in the middle is the only thing your ear has to catch.
On the staff
Major against minor
The whole difference between the two most common chords is one semitone in one voice. C major is C, E, G. C minor is C, E flat, G. The root holds, the 5th holds, and the 3rd drops a half step. Trained ears name a chord major or minor almost entirely on that middle note, so the first thing worth doing is learning to hear the 3rd through the chord rather than the bass or the top.
Where it sits in a key
In a major key the chords on the 1st, 4th, and 5th scale degrees are all major triads: I, IV, and V. Those three carry most of the harmony you hear in pop, folk, and classical music. The V chord pulls toward the I, and the I is home. Because the major triad is the sound of arrival, it is also the chord most pieces end on. Kostka and Payne weight the four triad types plainly: the major and minor are by far the most common in tonal music, and the augmented the rarest.
How Aubel handles it
Major is one of the two chords the Chords game starts with, alongside minor. The pair is the foundation, because the first skill the game trains is hearing major against minor, the single-note difference in the 3rd. Each round plays all the chord's notes together on a random root, so you name the quality rather than a key. Once the pair is solid, the diminished triad unlocks next, then augmented, then the five 7th chords.