Once upon a time, each country had their own currency. If a county's imports were greater than their exports, the value of the currency would tend to fall, which tended to increase exports (by making their exports cheaper) and decrease imports (by making imports more expensive).
This is called "floating exchange rates". The downside of this is that a business that imports raw materials and/or exports products, finds it difficult to set prices, or to plan ahead. It meant that, maybe you thought that you were in the business of importing tulip bulbs from Holland and exporting flowers to Spain. But you were also, willy-nilly, in the business of taking risks in exchange rates.
Before WW1, countries tended to tie their curency to gold, so for each country that did that, exchange rates were constant, which made international trade more predictable. Except that every now and then, pressures got too great, and a country had to devalue. You'll remember 1967 when the pound was devalued from $2.80 to $2.40.
After WW2, there was an international agreement to have fixed exhange rates. This collapsed in the 1970s. After then, exchange rates floated. How many dollars you got for your pound, was whatever value made the number of sellers equal the number of buyers. In other words, a market rate.
In 1999, 11 of the countries of the EEC (most notably excepting the UK, and now 19 countries) agreed to adopt a common currency, the euro. This made international trade between those countries easier and less prone to the foreign currency risk mentioned above.
So what happens if you're in the euro, but your imports are more than your exports? You'll have to borrow the difference. If you're a country, you're usually considered a good risk, banks are very willing to lend to you. But the more you borrow, the more you don't look like a good risk, until eventually, you run out of lenders.
So then you have to make special arrangements. You go to your creditors and say, "Choose one of these; 1) we default and you lose your entire loan or 2) you accept that we only owe you half of what we really owe you". This is called a haircut. In 2012, Greece persuaded their creditors to accept a 53.5% haircut. But as you can imagine, once someone has pulled that stunt, people are a lot less likely to lend to them for a long time afterwards.
The other thing you can do, is go to special sources of finance. In the UK, we have the Bank of England as the "lender of last resort", meaning when no-one will lend you money to go on trading. In the case of Greece, that would be the European Central Bank, or the IMF.
Hopefully, the haircut, plus the special finance, gives the country enough time to take measures to boost exports and cut imports; possibly they'll have to reduce public spending, economise in whatever ways they can (this is sometimes called "austerity") so that income and expenditure come back into balance.
If the country doesn't get itself back into balance. then it's back to the haircut and special finances.
Of course, there's only so many times that lenders wil lend money to a spendthrift when there's no apparent possibility of getting paid back. Do not blame the people who are no longer willing to lend good money after bad. Blame the spendthrift.
And that is now what's happened to Greece. So what's the solution? First, let's look at something that isn't a solution. A crowdfund is raising money, with the objective of raising 1600 million euroes. So far, they've raised 1 million.
And if you donate, for example, three euros, you're told that you'll get a postcard of the Greek prime minister, sent from Greece. Of course, the cost of the card and the stamp will eat up a fair chunk of that. And, of course, if the crowdfund doesn't add up to 1600 million euros, everyone gets their money back. The person who set it up says that this isn't a joke.
And, by the way, 1,600 million euros is just one piece of the Greek debt to the IMF. Total Greek debt to the IMF is 27,000 million euros. Total Greek debt is more than 320,000 million euros.
Now let's look at what is probably the only possible solution. Greece will have to leave the euro, and have their own currency, which I'd guess they'd call the drachma. The drachma would float against other currencies and find its own level.
And then what happens in Greece?
The first effect will be on the banking system. If the banks can't get euros, then they can't give euros to their depositors. And you can be sure that the depositors are right now keen to withdraw as much as they can, before the banks run out of funds - this is what is called "a run on the banks". Right now,, you're only allowed to take 60 euros per day from your account. That's maybe enough for food and necessaries, but not for much more. And, but the way, when the UK government bailed out our banks in 2008-2009,, it was to prevent exactly this situation. And the inability of consumers to spend, will deepen the Greek recession.
The move to drachmas will be total chaos. For a start, no-one will know what a drachma is worth, even after the Greek government says what they want it to be. Secondly, switching to a new currency is a horribly complicated business, and you can be sure that people with euro deposits in greek banks, will be given a compulsory, and substantial, haircut. And thirdly, it's all being done with very little notice, and not a lot of planning.
Greece - we wish you well. But you've run out of people willing to lend to you.