Ever since the signing of the Magna Carta in 1215, the power of the British Monarchy has been transferred to Parliament, the legislative body. (The two Houses of Parliament are the House of Lords and the House of Commons.) This arrangement is called a "constitutional monarchy," (although even here the term 'monarchy' very relative.)
The 'Queen' or 'King' nevertheless has an important representative function, which should not be underestimated. For example, Queen Elizabeth formally opens and closes all sessions of Parliament, and she is often called upon to represent Britain in diplomatic ceremonies, both at home and abroad.
The Queen does indeed have some political sway in foreign affairs, but her power is limited. For example, her "vote" to have native populations in the Indian Ocean displaced (in order to accord an American military base a more strategic location) was vetoed in an international court.
In his essay "Brave New World Revisited," Aldous Huxley observes that for all practical purposes, the current constitutional monarchy in Britain is actually more democratic in function than Congress in the United States!