Agreed with Brisbane Rhino, the basic concept of a derivative is just a form of insurance but the way they are used is totally inappropriate for insurance.
If you buy insurance for your house burning down then only you have insurance for it, if your house burns down then your insurer pays out for the damage (this is effectively the reason AIG went bust because of having to pay out many multiples of times when defaults they were insuring against happened)
But if this was done by derivatives, you could buy a derivative that paid out in the event of your house burning down....but also several other people could buy a derivative paying out in the event of your house burning down. So if your house burns down then you get the pay out but so do many other people. For you, you've lost your house and been compensated, but for the other people that also burnt derivatives based on your house burning down, they have just received a nice pay out and not suffered a burnt down house. The insurer has had to pay out multiple times so its bad for the insurer too.
Of course the other problem here is there are now many unconnected people that have a vested interest in your house burning down as they profit from it. In the concept of business and defaults, or mortgages and defaults, this can be a real problem if there are big financial players in the market that can influence that bad event happening.
Eg if I am a predatory lender I could make a mortgage loan to a borrower with a very poor credit history, that was a high risk of defaulting....if I could then disguise the risk of that loan and get ratings agencies to pass it off as AAA rated (which is what was going on), I might be able to sell that loan to someone else so now someone else has taken the risk. If I then buy a derivative that pays out in the event of that loan defaulting then I get a payout on default.
Alternatively if I was a major shareholder in a business and a key provider of finance to that business, I could buy a derivative that pays out in the event of the business going bust, and then suddenly sell the shares to prompt a tumbling in the share price, at the same time as cutting finance to that business, help make sure it goes under, then I get the payout from the derivative.
The widespread use of derivatives meant that there was a serious issue in terms of incentives at the top end of the financial services industry....the financial services industry is meant to be there to facilitate business and help keep it flowing, but once these derivatives were floating around there were a lot of major banks that had vested interests in individual businesses going bust, because that would trigger the payouts on those derivatives.