In a nutshell that is what is happening. The Greeks, along with the rest of the 22 Euro zone countries decided in 1999 to bind themselves to a common currency. This had both positive and negative aspects to it.

The good was quickly seen by the EU, the grand experiment seemed to be working. It encouraged tourism, made the whole continent more efficient and all but eliminated currency risk.
Currency Risk is basically this: a guy owes you cash in German Deutschemarks, but you have to pay all your bills in French Lira. Which is fine, you just exchange the Deutschemarks into Lira, and then pay your French debts. The problem develops when in a short period of time the D’marks you are going to receive rapidly fall against the Lira that you yourself owe. This makes business risky, and hedging against currency risk also has a cost.
The Euro eliminated this problem (and many others) and all was right for about 10 years. The EU had a strong economy, sure they ran deficits but the rate of economic growth and inflation kept it all manageable.

Here is the bad, when the Euro was adopted the participating countries gave up control of their monetary policy. This is a countries ability to say how much new debt they are allowed to issue.
In the past 5 years we in the United States have issued A LOT of debt to pay for all kinds of things. Most of this is due to a shortfall in tax receipts. The Europeans cannot do this. They are limited on how much debt they can issue to pay for things. When the Euro treaty was signed all the countries agreed to set standards and limits of how much of a deficit a single country could run.
The problem is their tax receipts are drying up too, and like the rest of us. The PIIGS (Portagual, Italy, Ireland, Greece, and Spain) are all pretty much broke. They have huge socialist societies and their government pays for a lot of things. In the past, when all these countries had their own currencies they would just issue more debt and cover the costs. Now that option is no longer open to them. They cannot borrow anymore money; they have to live like the rest of us.
Greece has already written down some of its debt, and has been bailed out several times by the ECB and IMF. The PIIGS are really painted into a corner, they can’t borrow any more money, and they can’t balance their budgets. The rest of the EU can bail them out, but it really seams it will just be throwing good money after bad.
You as a person can just declare bankruptcy and start afresh, it hurts for a little while but often it is the best course of action. Countries cannot really do this. They can default on their debt, but the results are rather catastrophic, and the consequences are much worse than having a poor credit score for a few years.
Moral of the story: I have no idea how to fix this, ECB has to let the Greeks issue more debt, or leave the Euro zone entirely. Neither of these options are going to be good for anyone.
