This commonly refers to a diplomat that has the full signing power and authority of their government. They can agree to treaties with other nations.
This position/title was more important before instant communication. Before long-distance, real-time communication was possible, the foreign representatives of a government might be incommunicado for months at a time, so they needed some amount of authority and self-governance.
Why I Looked It Up
Found in a passage about premature news of the signing of the armistice that ended World War 1.
…a telegram reached Howard from the United Press office in Paris: “Armistice report untrue. War Ministry issues absolute denial and declares enemy plenipotentiaries to be still on way through lines.”
Added on January 18, 2022
From a biographical sketch of diplomat George Bancroft:
Appointed minister plenipotentiary to Prussia by President Andrew Johnson in 1867…