Ministerial means having to do with a minister of a religion, or a government. If your dad is a pastor, he may have to make it clear if he is telling you not to lie as a father, or in his ministerial capacity.
Ministerial derives from the Latin minister meaning "servant." A religious minister is a servant of God. A government minister is the head of a department, but also a servant of the government. Their work is their ministry, thus ministerial means pertaining to that work. If, as England's minister of defense, you streamlined the military, that streamlining would be your ministerial legacy.
