The Great Offices of State are the four most important cabinet jobs in the United Kingdom.
Only one person has ever held all four, James Callaghan, who was Prime Minister from 1976 to 1979.
The four posts are
Prime Minister
Chancellor of the Exchequer
Foreign Secretary
Home Secretary
The King asks the Prime Minister to form a Government following a General Election. The Party who has the Majority in the House of Commons is usually asked to form.
The Chancellor, Foreign and Home Secretary are also appointed by the King. These are on the advice of the Prime Minister. Its more of a formality for the King to appoint as the decision is taken by the Prime Minister. This is the same for the other Cabinet Ministers.