The Greek financial system is in big trouble right now. The fundamental problem is that the Greek government has been on a bit of spending bender over the past few years and has borrowed a lot of money to pay for this, all of it denominated in euros. It has become frighteningly clear that this level of debt is unsustainable and the Greek government needs truly radical fiscal reform to avoid defaulting on its outstanding debt. Much of that debt is held in the form of Greek government bonds by Greek banks, but a large amount is also held by various financial institutions outside of Greece.
By itself this is not really a very interesting or important situation. There are a large number of countries in the world and inevitably, some of them get into fiscal trouble. Some sort of financial crisis of this sort happens on a fairly regular basis. Greece is, however, a member of a monetary union. And its financial health could have an effect on the financial health of other members of that union.
The euro is a unique currency because it is issued by a collection of sovereign states, rather than by a single country as is usually the case. The currency was formally introduced into circulation in 2002 and replaced the national currencies of the participating countries. Control of the euro money was given to the European Central Bank (ECB), which was created with the sole purpose of managing the euro. When the euro was created it was very clear that all member countries would be using a single currency and would therefore be unified monetarily. It was not clear, however, how unified these countries would be in fiscal terms, however. There is no governmental equivalent to the ECB. There is a European parliament, but there is no central government with authority to tax and spend for the European Union as a whole. Fiscal matters are, in theory, left entirely to the individual member countries. This means there is no natural central source of funds to "bail out" the Greek government. The two bailout packages worked out so far have been hammered out via complex negotiations between Greece, the ECB, and other European governments.
Suppose Greece decides it is going to default on its government bonds. Does this necessarily mean that the euro as a currency is in trouble? Not necessarily. In fact, if there is no expectation that Europe is a fiscally united, then there should be no issue at all. Greek bonds, though denominated in the same currency as German bond, already pay higher interest rates due to their higher probability of default. If the Greek government decides to default, things could get really bad for Greece, but it need not affect other European countries. The fact that German and other European banks hold Greek government bonds could lead to increased stress on the banking sectors in those countries, but it need not lead to dissolution of the euro as a currency.
However, a problem does arise with one the way that Greece might choose to default on its debt. Rather than default outright, the Greek government could choose to drop out of the euro zone and reintroduce their previous national currency, the drachma. They could do this by initially trading all euro amounts in Greece one-for-one with drachma, for example, and legally rewriting all contracts in euro to contracts in drachma. Then the Greek central bank could drastically increase the number of drachma in circulation and repay its nominal debt with this new money. The result would be a devaluation of the drachma. Greek assets would be worth less on the world market, just like a default, but a formal default would be avoided. In effect, Greece would be solving its fiscal problems by imposing an inflation tax and at least some of the burden of that tax would fall on non-Greek holders of Greek government bonds.
Now suppose you had a time machine and knew for certain that this was going to happen on Dec. 31st 2011. What should you do today? You should sell any Greek assets you hold today to avoid the inevitable loss in their value when the drachma is devalued. If you are a savvy investor you might take profits by short-selling Greek debt. Even if you don't have the time machine and are uncertain what is going to happen, you might still find it prudent to sell. When all or most investors do this, the result is a worsening of the financial crisis.
If investors feel that Greek devaluation is becoming more and more likely, it is only natural that they begin to look at other European countries with similar fiscal problems. These countries include Ireland, Spain, Portugal, and perhaps even Italy & France. If enough countries choose to withdraw and devalue their currencies - particularly if either of the latter two do - then the euro as a multinational currency will effectively be dead.
Greek fiscal problems don't automatically mean the euro is doomed, but it is very easy to see why policy makers in Europe and elsewhere are worried that events are moving in exactly that direction.
