Wikipedia
A promagistrate is a person who acts in and with the authority and capacity of a magistrate, but without holding a magisterial office. A legal innovation of the Roman Republic, the promagistracy was invented in order to provide Rome with governors of overseas territories instead of having to elect more magistrates each year. Promagistrates were appointed by senatus consultum; like all acts of the Roman Senate, these appointments were not entirely legal and could be overruled by the Roman assemblies, e.g., the replacement of Quintus Caecilius Metellus Numidicus by Gaius Marius during the Jugurthine War.
Promagistrates were usually either proquaestors (acting in place of quaestors), propraetors, acting in place of praetors, or proconsuls acting in place of consuls. A promagistrate held equal authority to the equivalent magistrate, was attended by the same number of lictors, and generally speaking had autocratic power within his province, be it territorial or otherwise. Promagistrates usually had already held the office in whose stead they were acting, although this was not mandatory.
One should also mention here the procurator, a posting originally as a financial manager in a province, a position which held no magisterial power until Claudius gave them his power in the mid 40s AD, enabling them to administer provinces.
The institution of promagistracies developed because the Romans found it inconvenient to continue adding ordinary magistracies to administer their newly acquired overseas possessions. Therefore, they adopted the practice of appointing an individual to act in place or capacity of (pro) a magistrate (magistratu); a promagistrate was literally a lieutenant. Subsequently, when Pompeius Magnus was given proconsular imperium to fight against Quintus Sertorius, the Senate made a point of distinguishing that he was not actually being appointed a promagistrate: he was appointed to act not in place of a consul (pro consule), but on behalf of the consuls (pro consulibus).
The Roman legal concept of imperium meant that an "imperial" magistrate or promagistrate had absolute authority within the competence of his office; a promagistrate with imperium appointed to govern a province, therefore, had absolute authority within his capacity as governor of that province; indeed, the word provincia referred both to the governor's office or jurisdiction and to the territory he governed. A provincial governor had almost totally unlimited authority, and frequently extorted vast amounts of money from the provincial population — he had total immunity from prosecution during his term in office. It became fairly common for provincial governors to seek continual election to office to avoid trial for extortion and bribery, two famous examples being Gaius Verres and Lucius Sergius Catilina.
The near limitless power of a high-ranking promagistrate has led to the term " proconsul" being used to designate any high-ranking and authoritative official appointed from above (or from without) to govern a territory without regard for local political institutions (i.e., one who is not elected and whose authority supersedes that of local officials). One of the most prominent examples of this is Douglas MacArthur, who was given vast powers to implement reform and recovery efforts in Japan after World War II, and has been described occasionally as "the American proconsul of Japan".