Anything diocesan relates to a diocese, which is an area that a senior Catholic priest is in charge of. You might see it in phrases like “diocesan newspapers,” “diocesan policies,” or “diocesan officials.”
If you hear this word rather than see it, its relationship to its root (diocese) may not be obvious because of the shift in stress. Diocesan is simply the adjective of diocese, the territorial jurisdiction of a Catholic bishop. The immediate root is from a Latin word for an “administrative division,” and that meaning is still important. All diocesan affairs relate to how the diocese is organized and run by Catholic officials and clergy under the bishop.