A viceroy is somebody who governs a country or province as a substitute for the monarch. The term derives from the Latin prefix vice-, meaning "in the place of" and roi, meaning king. A vicereine is a woman in a viceregal position, or a viceroy's wife.
For example when Spain controlled much of the New World, communications with the mother country could take months, so the King of Spain appointed Viceroys in Mexico City to govern New Spain and in Lima, Peru to govern western South America. One of the most famous and powerful viceregal offices in the world was that of the Viceroy of India during the British Raj.
In imperial China, viceroy was the English translation of the title "general supervisor-protector" of Chinese officials heading some large administrative divisions. For instance, there was a viceroy of Kwantung and Kwangsi, a viceroy of Hukwang (the combination of the provinces of Hubei and Hunan). Li Hongzhang was viceroy of Hukwang from 1867 to 1870.
From 1858 to 1947, the Governor-General of India was informally known as the Viceroy. The adjective viceregal is used in some Commonwealth Realms to refer to the function of the Governor-General as representative of the Crown.