Diminished is actually the name of a chord and a scale.
The diminished scale in C contains for example the notes
C, Eb, Gb (and A).
The scale contains C, D, Eb, F, Gb, Ab, A and B.
The diminished tuning for diatonic harmonicas has the same order of notes (with the typical whole note / half note structure).
This structure makes it possible to reach all chromatic notes with the help of the bending technique alone. It is not difficult to learn, but exact intonation needs a lot of practice.
The advantage over regular chromatic harmonicas (which can be tuned in diminished as well) is in my opinion the more powerfull and dynamic sound of the diatonic Diminished.
The ordinary 10 hole Blues harmonica is tuned according to the Richter-System. It is designed to play songs, which remain inside the harmonic setting of one scale. Other songs in other keys require more harmonicas. To cover all 12 keys, the average Richter player needs (at least) 12 instruments.
For songs with more complex chord changes (appearing in genres like Jazz, Tango, Latin or even some Pop and Rock songs), the Richter tuning is extremely hard to handle.
My recommendation: everyone who is interested in playing these styles should give the dimished tuning a try.