The Queen of England, presently Queen Elizabeth II, is the monarch of 16 Commonwealth realms including the United Kingdom, and has different roles and powers.
The Queen of England largely has ceremonial powers, but that does not mean she does not influence major decisions. She does have a lot of power. Most of it is just potential power though. The Royal family does play an active role in the democratic process. They take on a lot of ceremonial and diplomatic duties.
The Oxford Dictionary defines power as "the capacity or ability to direct or influence the behavior of others or the course of events". And the queen, who recently celebrated her diamond jubilee, sure has a lot of it!
★ The powers bestowed on the Queen or the Monarch are called Royal Prerogative. It is hard to determine the extent of these powers, as most are just ceremonial.
★ The Queen appoints the Prime Minister after the general election or resignation. The decision is made with the support of the House of Commons. She can remove the Prime Minister by dissolving the Parliament.
★ She has weekly meetings with the Prime Minister, which are very confidential, and no records of these are kept.
★ She can encourage or warn the ministers, and can be consulted on important matters through the Prime Minister. She can appoint and dismiss ministers, and summon or suspend the Parliament.
★ The Parliament cannot open without the Queen's Speech. She addresses both the houses through her speech, which is actually written by the Government, and not the Queen herself. It gives an outline of the Government's policy in the upcoming session.
★ The bills passed in the Parliament do require the Queen's consent before becoming laws. But a case of the Queen refusing Assent hasn't happened since 1707.
★ She regulates the civil services, issues passports, can negotiate, sign, or terminate agreements, but cannot alter laws. British passports are issued on Her Majesty's name, although nowadays ministers issue these.
★ The Queen has the power to declare a war or make peace, but this is usually done by the Prime Minister. Her Highness is above the law. No civil action can be taken on the Queen of England.
★ The Queen has the power to grant various honors to the citizens. She can issue orders of knighthood.
★ The Queen does not have much judicial power, but she can use Royal Pardon to withdraw a death sentence. This can only be done if the convict is wrongly sentenced.
★ Queen of England is the Commander-in-chief of the British Armed Forces, Head of the Commonwealth, and Supreme Governor of the Church of England.
★ An oath of allegiance to The Queen is sworn by the members of Armed Forces. The Queen can commission officers, and has a lot of control over disposition of the Forces. They are known as Her Majesty's Armed Forces.
As you can see the Queen does have a lot of power, but she does not necessarily exercise it. Most of it is soft power.