In many republics, power is split between the federal government, which oversees the affairs of the nation as a whole (things like the military, foreign policy, etc), and provincial government which are local governments meant to deal with smaller issues like education, housing, etc.
The national government is the main pillar of a nation, and it´s main function is to direct, control and manage it´s internal institutions. Provincial is an adjective that helps us to refer anything that is linked to a province. A province is an administrative division that exists in certain countries that is equivalent to the states or departments of other nations.
The provincial government will always be supervised by the national government.