Diminished 7th chords are wonderments that do so many different things in music — they are nearly inexaustible. There are only 3 diminished 7th chords because all the rest are simply inversions of those 3.

You can use dim 7th chords to modulate to a different key, to locate clever chord progressions, and as doorways to get you to dominant 7th chords, minor 6th chords. major 7th chords, and on and on.

There are 4 notes in each diminishted 7th chords, each a minor 3rd away from the previous note. Any note in a dim 7th chord can be the root of the chord, so every dim 7th chord can function as 4 different chord names.

Listen to this podcast and you’ll get the idea: