There are many and varied reasons why the rich get richer and the poor get poorer. Some of these reasons are rather mundane
; the boots example quoted by Demeter
above has always been one of my favourite bits of economic theory. There are also certain financial modes of operation that exacerbate this process: specifically, interest rates
Take a thousand dollars for example - in itself it's not a dynamic entity. But throw a bank into the mix and that thousand will start to grow, because it is most likely in an account that accrues interest. Now, if you are $1,000 in credit, the interest will be incurred by the bank and credited to you: you will be getting richer by doing nothing. However, if you are $1,000 in debt, the interest will be incurred by you and credited to the bank: you will be getting poorer without spending anything.
The same basic process applies to national debts and is at the very core of the Third World debt problem. The vicious cycle works very much in the way that LordLiverpool describes above; however, what he fails to take into account is the fact that this cycle was not kick-started by the evil, cynical, incompetent Third World governments (and don't get me wrong, some of them are all of the above and more to boot). It was put in place by the World Bank when it gave countries loans it knew they will not be able to service, at interest rates many times higher than those available to powerful economies, and with such conditions attached that no entity that was not desperate for cash would ever have agreed to. It basically played the loan shark: lend them more money than they can repay, then forcibly take them for all they've got. The World Bank is basically asset-stripping Africa right now, and the UN is helpfully providing the muscle in the form of "peace" keeping troops.
It doesn't stop there, though. What people rarely consider in these sorts of debates (and their siblings, debates about the evils or otherwise of capitalism and the free market) is that the processes operating on the rich and the poor are interconnected. In other words, he poor get poorer because the rich get richer. To put it even more bluntly, the rich get richer by taking money away from the poor.
Some examples are glaringly obvious: if you are a company owner, you are most likely richer than your employees. You have the power to cut their wages and benefits, but they have no direct influence on your bank balance. You can - and probably would as soon as look at them - make them poorer. If you are a head of state in a G8 country, you can levy protectionist tariffs on goods imported into your country, bankrupting Third World producers, and there's nothing they can do about it - they have no leverage over you, because you have money and money is power (literally in the case of countries with fat "defence" budgets).
But we rich people in the West rob the poor of this world, including the poor of our own countries, in a more subtle way. We do it by exercising our right to better choice and value in our role as consumers. When we shop around to get the best price, we force companies to lower their costs in order to absorb the cut in profit margins. The most popular way of doing it (more even than cutting on security procedures, despite what Fight Club may try and tell you) is to cut wages. Since most people employed in manufacturing are already poor, by getting good value for our trainers, cars, frozen burgers and CD players we the people who can afford those goods are making them poorer.
It gets worse. When we elect governments who promise us lower tax on fuel, we inadvertently make them drive a harder bargain with the producers of oil - many if not most of whom are considered less than fully industrialised economies - because nobody, not even the government, likes to take a cut in revenue. It's much easier to go to war with Iraq to force oil prices down without actually cutting taxes. When we refuse to spend the extra £0.20 on a bar of Fair Trade chocolate, we are both directly and indirectly shooting small farmers in the leg, and they are by far the world's poorest sector. When we come to expect, even demand, uniformly low prices in a restaurant, we get McDonalds.
People are always telling me that my personal consumer boycotts and endorsements are a waste of time, that I am not making any difference, that the big companies who are responsible for the ravages of the unFree Market don't listen to the tiny minority that I am part of. Like I care. What I want is to be able to sleep at night, and I know I couldn't do that if I thought that I had robbed some starving child in Ghana even of a fraction of a cent. It's not much to me, but over the span of my entire consumer life it will be a hell of a lot to them. Think about it this way: I can’t prove to you that a person died because you bought that cheap, over processed Haitian sugar that was bought at starvation prices from desperate farmers; but you can’t prove to me that a person didn’t. So just to be on the safe side, I urge you to stop helping the big corporations and the powerful governments to force the poor deeper into poverty.