Short answers, pulled from the story.
A Roman diocese was a regional administrative grouping of several provinces within the Late Roman Empire, dated roughly from AD 284 to 641. It was created to maintain the link between the imperial center and the individual provinces after Diocletian multiplied the number of provinces from 48 to around a hundred. Each diocese was governed by a vicar who supervised provincial governors and heard appeals from provincial courts.
The Roman Empire was initially divided into twelve dioceses, rising to fourteen by the end of the fourth century. The largest single diocese was the Diocese of the East, which encompassed sixteen provinces.
Each Roman diocese was governed by an official called a vicarius, or vicar, who was appointed by the emperor and accountable only to him. The vicar controlled provincial governors, administered tax collection, and judged appeals, but held no military command over troops stationed in the diocese.
Justinian abolished the dioceses of the East, Asia, and Pontus in 535-536, and abolished the diocese of Egypt in 539. He re-established the diocese of Pontus in 548 due to internal disorder. His stated reason for the abolitions was that the vicars had become superfluous because their courts of appeal were used less frequently and provincial governors could be overseen directly by the Praetorian Prefect.
Roman dioceses declined for several reasons: Constantine's creation of regional Praetorian Prefectures bypassed the vicars by allowing prefects to deal directly with governors; the shift to collecting taxes in gold reduced the administrative paperwork that justified the middle tier; and Justinian abolished most dioceses in 535-539. The final disappearance came in the seventh century as Arab and Slav invasions destroyed the territorial base of the remaining prefectures, and the new theme system replaced the old civilian-military separation entirely.
The Franks and Burgundians left no evidence of maintaining the Roman provincial system. The Visigoths and Vandals kept the provinces but not the dioceses or prefectures. In Italia, Odoacer and Theoderic preserved the Roman provincial apparatus almost intact, including the Praetorian Prefecture of Italia and both Italian vicariates, because they held their positions officially as viceroys of the emperor in Constantinople.