Hinges. (Latin, cardo.) The election of the Pope “hinges” on the voice of the sacred college, and on the Pope the doctrines of the Church depend; so that the cardinals are in fact the hinges on which the Christian Church turns. There may be six cardinal bishops, fifty cardinal priests, and fourteen cardinal deacons, who constitute the Pope's council, and who elect the Pope when a vacancy occurs.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Cardinals from Fact Monster: