The following is how a recent Bloomberg article defined derivatives....
Most people have no idea that Wall Street has become a gigantic financial casino. The big Wall Street banks are making tens of billions of dollars a year in the derivatives market, and nobody in the financial community wants the party to end. The word "derivatives" sounds complicated and technical, but understanding them is really not that hard.
A derivative is essentially a fancy way of saying that a bet has been made. Originally, these bets were designed to hedge risk, but today the derivatives market has mushroomed into a mountain of speculation unlike anything the world has ever seen before.
Estimates of the notional value of the worldwide derivatives market go from $600 trillion all the way up to $1.5 quadrillion. Keep in mind that the GDP of the entire world is only somewhere in the neighborhood of $65 trillion. The danger to the global financial system posed by derivatives is so great that Warren Buffet once called them "financial weapons of mass destruction". For now, the financial powers that be are trying to keep the casino rolling, but it is inevitable that at some point this entire mess is going to come crashing down. When it does, we are going to be facing a derivatives crisis that really could destroy the entire global financial system.
Most people don't talk much about derivatives because they simply do not understand them.
Perhaps a couple of definitions would be helpful.