General equilibrium theory is a branch of economic theory that examines how supply and demand interact across multiple markets simultaneously to determine prices and allocate resources efficiently. It seeks to understand how various markets in an economy are interconnected and how changes in one market can affect others, ultimately aiming for a state where all markets are in balance, or 'equilibrium'. The concepts of the Edgeworth box and contract curve illustrate the efficiency of resource allocation and trade between two agents, showcasing how general equilibrium can be achieved through voluntary exchange.