You're broadly right. The British Royal family generally have few legal roles apart from the Queen herself, although they are immune from various laws like planning permission (local government has to authorise that any building work is safe, but the royal family can do what they like).
The Queen is in name the Head of State, the head of the armed forces and the head of the Church of England. In practice she is not allowed to actually exercise any authority or even display any preferences. The cost of keeping the whole royal family is estimated as £41.5m (about $70m?) per year, although this is not all as cash paid directly to them (only £7.9m) - a lot of it goes as money spent upkeeping the various estates. In addition there is the cost of security provided by the police and the army, which is not published.
However, this money is offset against money paid to the treasury in income tax, capital gains tax (in the UK, if you buy property cheap, and it goes up in value and you sell it expensively, this difference is subject to capital gains tax), and in earnings from various estates they own - these earnings are paid to the state in exchange for the £7.9m mentioned above. The Royal family own an enormous amount of land. One set of land alone, the Crown Estates, is worth £6.2 billion, and makes profits of around £200m per year which are paid to the state, which alone heavily outweighs the cost of the Royal family. In addition there are the Duchies of Cornwall and Lancaster which are probably worth another £1bn.
From our point of view, financially, it benefits us to have these holdings associated with the state rather than a private business, as a lot more money flows back into the state than it would do otherwise. Most of their wealth is based on stuff they inherited, or proceeds from the estates, or businesses based on the estates. Prince Charles owns a company that makes biscuits (Duchy Originals). They're quite nice!
Politically, the point of keeping the Queen as Head of state is to provide some sort of counterbalance, albeit even only theoretical, to the Prime Minister. Most countries have two houses of government and a Head of State; the US has the House, the Senate and the President. The British Prime Minister controls the House of Commons (roughly equivalent to the House); the House of Lords (even more roughly equivalent to the Senate) is much weaker than the Commons; so he actually has much more direct authority than the President of the US, so it's important that there is some counterbalance. The British PM cannot actually seize power as a dictator because technically the army belongs to the Queen and she has the authority to dissolve parliament. The Queen cannot seize power because it would cause a revolution.
This situation has basically evolved over the last 350 years or so because, as revolutions happened all across Europe and various Kings and Queens were beheaded, the British Monarchy looked at it and thought, we would rather give power back a bit at a time, than suffer a revolution and lose it all. The ball was started by our own Civil War, 1642-1651, followed mainly by a period of dictatorship, until we re-established a monarchy that had to listen to parliament in 1660. This gradual constraining of the monarchy has continued right up until 1992 when they started paying income tax.
So - what's the benefit of keeping them? People have different opinions and it kind of comes down to taste. From my point of view the finances are pretty even or actually profitable for the country. For me it's a matter of style. For me, there is no other person in the world whose title is as impressive as the King or Queen of England. For sheer grandeur and symbolism nothing can touch it. The President of the United Stated comes second - but to be honest, he's only going to be there for eight years, and there is a reasonable prospect that one day Sarah Palin could have that title.
I think history and symbolism are important, especially in trying to create a nation; trying to make millions of people who don't know each other unite under the same banner. That is why America has worked so hard to elevate the idea of the President to an almost religious status. If you have something that's richly symbolic and you throw it away it's hard to build it up again.
I'm not especially into these particular people. I'm sure they're no better or worse than a lot of other people. But the idea of the monarchy is so central to the idea of what it means to be British, that, at a time when we're struggling for an idea of national identity as it is, it would be too destructive to rip it out. And they don't actually do any harm or cost any money.