So, a basic primer here. The US government currently spends more than it earns. It borrows the money to make up the difference by issuing treasury bonds. What happens is people (or countries) wanting to invest in a safe asset will loan the US govt money by buying these bonds when the treasury has an auction. China buys 'em, and so do your rich relatives... and so do some of the mutual funds in your 401(k). The federal government borrows this money in terms of anywhere from 30 years to just a few weeks. The problem lately is that people have been screaming about the fact that the Federal Reserve (the US's central bank) has been buying the bonds that the treasury issues. It's true and, so, in effect, the government is loaning itself money.
What people don't realize is that the government does this quite often. Have you heard sometime on the news that the Fed has raised or lowered interest rates (actually called the Federal Funds rate)? What the Fed is doing is actually buying bonds in the open market (when it lowers rates) and selling bonds (when it raises rates). The interesting thing is that the Fed can just increase the money in its own account electronically. When it wants to buy some bonds, it increases the funds it has on hand (with a keystroke) and places bids in the open market. New money suddenly enters the economy, and, since the interest rate is essentially the price of money, when there's more of it, interest rates decrease (it's supply and demand, just like everything else).
Lately, however, the Fed has been doing something a little unusual. It's called quantitative easing. Whereas the Fed is usually targeting the short term interest rate by buying short term bonds (remember, they go from a few weeks to 30 years), with quantitative easing the Fed is trying to lower long term interest rates (buying buying longer term bonds). This would affect things like mortgage rates, as those are usually tied to the 10 year treasury bond interest rate. The Fed reasons, rightly, that lower borrowing costs will entice people to spend more money. It's a tool from the nether regions of the tool bag, but with the Federal Funds rate at 0-0.25%, they couldn't take that any lower and had to change tactics. So, that's what quantitative easing is and how it's supposed to help the economy. Economists are actually split on how big an effect it has had, so it's anyone's guess, really. While some people (politicians included) are concerned with runaway inflation (THE GOVT IS BUYING ITS OWN BONDS!!!), the markets' outlook for inflation over the next 1-30 years has remained quite anchored. This is largely because the new money is just sitting there, instead of moving through the economy. Everyone is too scared to spend.