(copied from thing I wrote on another thread)
...when you hear they amount to more than the GDP of the world, are that a) a great many of these derivatives extend far off into the future; they are contracts about stuff that may happen in the future, but don't represent claims that can be called in in the present; and b) a great many of those contracts either cancel out or will never be payable and are thus void.
If you think of a derivative as being like a bet, imagine you called your bookmaker and said 'I want to bet $100 that UFOs will land on the White House lawn and conduct a bake sale between now and December 31 2012.' your bookmaker laughs and says 'sure buddy, I'll give you a million to one - if it happens, I'll pay you $100m.'
Well now the bookmaker's outstanding exposure is $100,000,000 (plus whatever other bets he has open) but the chances are that he will never have to actually pay this. Of course, if you worked closely with the President or the Joint Chiefs, he might not be so willing to take this bet, in case you knew something he didn't.
There are many derivatives that work the same way. I really don't expect the price of oil to hit $400 within the next decade...but there's a very slim chance it could. So I could insure against that possibility by taking out an option that would pay out of the price of oil actually went up that high, and I can get that option for very little money because the chance of it paying out is considered quite remote.
On the other hand, if I feared the price of oil would increase by 1% and my business was operating on razor-thin margins, then the option would cost me a bit more because a 1% price change is not very unusual.
So when you hear about 'trillions of dollars in outstanding derivatives', don't think of them as bills which have to be paid, but more like lottery tickets - some of which have a very big chance of becoming payable, and some of which have very little chance. the outstanding amount is what would be payable if every single one of those lottery tickets paid off at the same time, but that could never actually occur (because bets that something will not happen and bets that it will cannot both be correct).
...
To expand on this, imagine a bet on a horse race (the horses are an analogy to different companies, or the prices of different commodities - don't over think it :-) ).
There are 5 horses, with different odds:
A: 3-1
B: 2-1
C: 5-1
D: 4-1
E: 8-1
OK, imagine 50 people place bets, and just by chance they all bet $1, with 10 people betting on each horse so the total liability of the bookmaker is $80 (the maximum payout if E wins), and his actual exposure is $30 (because he took in $50 in bets); more likely A or B will win and the bookmaker will payout $30 or $20, and keep the rest as profit. Every race he keeps some of the profit and sets some aside in case of needing to pay out on the long shot (or if he can't cover that, he places a bet with another bookie).
But the total of all the possible payouts written down on the 50 betting slips is $220 ($30 + $20 + $50 + $40 + $80). So that's 4.4 times more than the total amount of money put down, and 2.75 times more than the largest amount the bookmaker might possibly need to pay. As soon as the race is finished, 10 people will go back to collect their winnings and the other 40 people will tear up their betting slips, which are now worthless.
So the $220 would be referred to as the nominal value of all the outstanding betting contracts before the race, but this sum will
never actually have to be paid out - not even close.
Here's a more technical explanation, which is fairly up to date and also discusses some of the risk factors:
http://www.ennisknupp.com/Portals/0/whitepapers/Introduction%20to%20Fixed%20Income%20Derivatives.pdf