In your article you hint at, without directly explaining, fractional reserve lending. As @achim03 describes in his response, this is what allows banks to create money out of thin air. Yes, the bank has to have some amount of "real" money in reserve to cover the amount of the loan, but it is typically a very small fraction of the loan. That loan can then be deposited into another bank and that bank need only cover a fraction of the amount deposited. As a loan is payed back the money simply disappears--except the interest, because the interest was not created as part of the original loan. I have heard arguments that this in party why we have a boom and bust cycle: fractional reserve lending creates principle, but not interest. This short film gives a simplified version of the process:
Be sure to see the filmmakers site for his response to two criticisms of the movie: http://paulgrignon.netfirms.com/MoneyasDebt/disputed_information.html
RE: What is money? Part 1 of a crime exposed