See the British monarchy is one of those rare and glorious places where the 'Head of State' is different from the 'Head of Government.' The Head of State gets to do all the ceremonial things that grant public legitimacy to the government -- you know, like parachuting into the Olympics, or more importantly accepting resignations, implicitly approving laws (by not vetoeing), meeting other country leaders for tea and crumpets. The Head of Government, aka Prime Minister, is the one actually driving the goddamn boat.

Americans: It's essentially a system where Barrack Obama doesn't have to take his family to China for 'vacation,' because he'd have a guy for that. Or if you prefer, it's a system where George W. Bush is in his office when 9/11 happens, instead of reading books to kids in a public school. Those are 'Head of State' ceremonial-type functions that a british Monarch would cover.