On another forum I go to, this question kinda popped up, and since one smart Aussie political/legal obsessed guy answered it so well, I think I'll just post it for your perusal:
The British Monarchy is a curious institution, as it exists in the Commonwealth nations that still have her Majesty as Queen. Strictly speaking, your statement [that the Queen holds no real power in England] is flat wrong. The Queen holds immense official power and exercises it on a daily basis.
I'll discuss the British version first.
Britain has a governmental rule called Parliamentary Sovereignty. This means that it is not the people who have ultimate power, but Parliament. Since Parliament is elected, that means essentially that the people decide who makes up their Parliament, but the Parliament is the one in control.
The Queen is a part of Parliament. She is the font of all executive power in the United Kingdom. She has and holds terrifying powers of criminal sanction, administrative decision, justice, (The Queen cannot be charged with a criminal offence, as criminal sanctions are HER laws), war, and other prerogatives of Kings stretching back to William the Conqueror.
This is embodied in a concept called "The Crown." It's not so important for England and Wales but it gets messy in Australia, which is why it's called "The Crown" and not "The Queen."
"The Crown," along with "The Lords" (Who hold their power from the Magna Carta) and "The Commons" (Not Commoners, but the regions of England) make up the Parliament of the United Kingdom. In order for any law or any executive power to be exercised, PARLIAMENT must agree. That means for the Queen to exercise any power she holds as "The Crown," she has to get Parliament's permission.
Since it is an inviolate rule of the British body politic that the Government is the group of people who control the House of Commons, combined with the concept of Parliamentary sovereignty, means that, in essence, The Queen holds total executive power in the United Kingdom but cannot exercise it without the approval of the democratically elected representatives in the Commons.
Why do they do things like this? So Prime Ministers don't get ideas that they can, themselves, usurp executive power for the sake of some idea that they've been "popularly mandated" to do so. David Cameron can't do whatever the hell he likes, but he's not restricted by a constitution in the way Pres. Obama is; he's restricted by the fact that as First Lord of the Treasury he has no right and no powers to do anything other than through Parliament. He officially has no powers. Neither can her Majesty, because she needs Parliament's permission to do anything. That's why she appears powerless. Because we, the people, elect our Parliamentary Representatives, who are the legislature, and are the only people who allow the executive (The Queen) to exercise her executive powers, it just so happens that we "tap into" the power of the Queen and use her executive powers through our elected legislators in Parliament whenever we want to do anything executive.
Australia and Canada have slightly different situations, because in Australia and Canada, the Queen gave her "The Crown" powers to the Governors-General, and further, split the executive and legislative powers of the British Parliament amongst a Federal and "provincial" Parliaments in each country. As a result the Commonwealth Parliament of Australia can't pass certain laws because they don't have "The Crown" power to do so because the Queen didn't give the Federal Government those powers. The States hold those.
In my personal opinion it's the best liberal constitutional system in the world- supreme power is vaguely rested in a person who cannot use those powers without the people's consent. And they're not written down like in the Constitution; each time the executive wants to do something, it has to ask Parliament, because they don't have a right to do ANYTHING otherwise. You know how Obama can make Presidential decrees or directives? Direct the forces of the United States without Congressional Approval? Make Recess Appointments? Doesn't have to answer to anybody except every 4 years?
Yeah, Queen can't do that. She has the power to do it, but she needs Parliamentary approval for each individual action because she has no powers she can unilaterally exercise.