Explain the system of Administration governed …

In ancient Rome, provinces were generally governed by politicians of senatorial rank, usually former consuls. A later exception was the province of Egypt, incorporated by Augustus. After the death of Cleopatra it was ruled by a governor of equestrian rank only, perhaps as a discouragement to senatorial ambition as Egypt was considered Augustus’s personal property, following the tradition of earlier, hellenistic kings.

The territory of people who were defeated in war might be brought under various forms of treaty, in some cases entailing complete subjection. The formal annexation of a territory created a “province” in the modern sense of an administrative unit that was geographically defined. Republican provinces were administered in one-year term by the consuls and praetors who had held office the previous year.

Rome started expanding beyond Italy during the First Punic War. The first permanent provinces to be annexed were Sicily in 241 BC and Sardinia in 237 BC. Military expansionism kept increasing the number of these administrative provinces, until there were no longer enough qualified individuals to fill the posts.
The terms of provincial governors often had to be extended for multiple years, and on occasion the Senate awarded imperium even to private citizens, most notably Pompey The Great. Prorogation undermined the republican constitutional principle of annual elected magistracies, and the amassing of disproportionate wealth and military power by a few men through their provincial commands was a major factor in the transition from a republic to imperial autocracy.