A viceroy is somebody who governs a country or province as a substitute for the monarch. The term derives from the words vice and royal. A viceroy's wife is called a vicereine.
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 viceroy offices in the world was the Viceroy of India during the British Raj.
In imperial China, viceroy was the English translation of the title (督護 or 總督) 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.
