The shape
A C diminished triad is C, E♭, G♭. Three notes, each three semitones apart. That equal spacing is unusual. Major, minor, and augmented triads all have at least one uneven gap between their notes. The diminished triad doesn't, which is why it sounds suspended and symmetric.
Stack one more minor 3rd on top and you get a diminished 7: C, E♭, G♭, A. Four notes, all three semitones apart. The full diminished 7 has no clear top or bottom; every inversion sounds identical, which is part of why it's such a useful pivot chord in classical voice-leading.
Where it lives naturally
Every major key contains one diminished triad: the one built on the 7th scale degree. In C major, that's B diminished (B, D, F). Classical theory calls this the leading-tone triad or vii°, and its job is to push back to the tonic. It contains the same tritone (B to F) that sits inside the dominant 7 chord (G7 in C major), which is why composers sometimes use vii° as a substitute when they want the pull without the V chord's heavier weight.
Every natural minor key also has a diminished triad, built on the 2nd degree this time. In A minor it's B, D, F again. Classical theory calls it ii°. It's the diminished half of the minor-key ii-V-i you hear in jazz standards.
How to hear it
The diminished triad sounds darker than minor but more focused than raw dissonance. Two of its notes form a tritone, which is unstable on its own. The middle note (the minor 3rd) sits in between and softens the tension by giving the ear somewhere to land on the way through. The chord doesn't read as harsh. It reads as mid-sentence.
Telling it apart from the other dark chords
Versus minor: both have a minor 3rd on the bottom. The minor chord puts a perfect 5th on top; the diminished puts a tritone there. Listen to the top note. If it sits comfortably, you're on a minor chord. If it leans outward, diminished.
Versus augmented: both are symmetric, both are unstable. Augmented stacks two major 3rds (a brighter, stretched sound). Diminished stacks two minor 3rds (compressed and darker). Most people who can hear major versus minor can hear augmented versus diminished by the same logic.
Versus half-diminished: the half-diminished is the same triad with a minor 7th added on top. That added note softens the chord and gives the tension somewhere to partially resolve. If the chord sounds like it's half-arrived, you're hearing half-diminished, not the bare triad.
The voice-leading reason it's so useful
The diminished triad sounds urgent because two of its notes are pulling toward specific targets. In B° inside C major: B (the leading tone) wants to rise to C, F (the 4th) wants to fall to E, and D can either rise to E or stay put as a common tone. The resolutions are built into the chord. Classical writing leans on this constantly when the composer wants to land on the tonic without the full weight of a perfect cadence.
How Aubel handles it
Chord training starts with major and minor. Once you're consistent on those, diminished is the next to unlock. The mental shortcut that tends to settle the sound fastest is "minor with the top note pulled in a semitone." Aubel weights newly-unlocked chords a little heavier for the first few sessions after unlock so the sound has time to register.