It’s a literary form. You could rewrite the sentence as “Le diocèse de Digne est un diocèse fatigant”, and it would have the same meaning. “que” refers back to “diocèse”. It allows inverting the order of the sentence (the subject is at the end).

It is just the common introducer C’est … qui …/C’est … que … with an additional omission of the verb in the relative clause. The verb should be est and thus:

C’est un diocèse fatigant qu’est celui de Digne.

Just as we could have

C’est un diocèse fatigant qu’a reçu M^gr Bienvenu.

Such omission is often made when there is a repetition but happens also with those who have little meaning such as être or se trouver.

It can happens with relative clauses introduced by other pronouns. A few other examples given by Grevisse

Il leur restait environ dix mille francs de rente, dont deux mille trois cents à lui. (Flaubert)

En bas, une sorte de caveau, au milieu duquel un trou pareil à l’ouverture d’un puits. (R. Escholier)