The title is sarcastic - the people who think derivatives are evil are people who don't understand them. "Derivatives" refers to a wide range of instruments, some of which are very simple and easy to understand and hard to abuse, and some which are very complex and/or easy to abuse. I think the misunderstanding leads to unfortunate threads like this.
There are 2 1/2 basic kinds of derivatives:
Forward contracts are agreements to buy/sell something in the future. For example, if I want oil three months from now, I can buy a contract from someone and they will sell me oil three months from now - at an agreed price.
One benefit: if I know I'll need oil in three months, rather than worry about the price shooting up to $600, I can buy this contract now, and I know exactly how much I'll have to pay in three months. Likewise, if I want to sell corn in three months, and I'm worried about the market crashing to $0.10, I can get someone to agree to buy it from me for a current, reasonable, agreed upon price.
Now, is that really evil or mysterious in any way? I don't think so, but when people talk about derivatives, they're including in that word things as basic as forwards.
Options are agreements where the buyer has the right to buy/sell something in the future. Unlike a forward, I don't have to buy oil from you three months from now at the price we agreed on - if the market price is much lower then, I'd rather buy it on the open market and I won't use my option.
The benefit: Instead of being stuck paying/receiving a price that may be much higher or lower than what I can actually get on the market, I can choose not to exercise the option (exercising means, actually choosing to buy/sell at the price you wanted originally).
Options are far more fascinating (in my opinion) than forwards since they lead to cool mathematical shit like Black-Scholes
Now, I don't think that's very complicated or evil either (but then again, options are my specialty).
Swaps are agreements where someone agrees to pay/receive several times for something. Most swaps are interest rate swaps (in fact, the majority of all derivatives by notional value are interest rate swaps - even though most people have never heard of them...maybe people should) but interest rates are boring and...easy to understand but long to explain. I could get into LIBOR and eurodollars and crap like that but I'm yawning already just saying LIBOR.
So I'll give an example (albeit rarely used): say I need oil every three months. I can get a swap on oil - every three months I can pay for oil for a fixed price. Sometimes I'll win (the market price may be much higher) and sometimes I'll lose (I would rather buy it much cheaper on the market then) - hence "swap".
This is the 1/2 in the 2 1/2 kinds of derivatives: a swap can be built as a series of forward contracts. Instead of having this swap, I could have a forward contract buying oil 3 months from now, another buying oil 6 months from now, and so on, and it would do the same thing. But by convention, swaps are thought of as special and different from forwards (except to arbitrageurs and this aforementioned travesty of a thread)
The jargon file on derivatives
The examples used above were all about oil. This is called the underlying of the derivative. Derivatives are all about being derived from something, the something is the underlying.
The notional value of a derivative is not how much it's worth or how dangerous it is. The notional value is what it is based on - for instance, the notional value of the forward buying crude oil for $100 is $100 - the gain/loss of the contract is whatever the difference is between the price of oil and $100. For an interest rate swap, the notional value is extremely different from its actual risk and value. An interest rate swap on $10 billion in notional value (that is, $10 billion in bonds more or less) will probably only lead to a fraction of a percent of that in actual money changing hands due to changing interest rates. Potentially, yes, it could be $10 billion changing hands (it could be also much more if rates go the other way in the absurd extreme) but in all normal circumstances the actual value is tiny compared to the notional value for IRS.
While not going too far into overall finance, it's important to understand some concepts. One is asset class. Asset classes are categories of financial stuff: "equity" is an asset class that includes stocks, "fixed income" is an asset class that includes bonds, loans, and mortgages, "commodities" includes things like crude oil, corn, and iron.
The above examples of derivatives were examples of derivatives on commodities, because I think derivatives on commodities are clear to understand. One can just as easily imagine forwards, options, and swaps where the underlying is IBM (equity) or US treasury bonds (fixed income).
Derivatives: the evil/mysterious parts
The reason I mentioned asset class is because there are some kinds of derivatives which are special to fixed income assets (bonds/loans/mortgages) that have special features. "Special features" to a programmer means "a bug".
Credit default swaps (normally called just CDS) look like swaps. A CDS is a form of insurance - every couple months you pay something, and if the thing you have insurance on goes bankrupt, you get a huge payout.
Example: If I sold a CDS on Lehman Brothers in 2008, the buyer would pay me every couple months, then when Lehman went bankrupt, I would have to pay a ton (like normal insurance; the actual payout is buying at par the company's bonds even though they're almost worthless, so it almost has optionality features).
Although this looks like the crude oil swap I mentioned above (periodic payments/receipts) the "almost always payer" feature combined with the "massive potential receiver" feature is totally unlike most swaps. This feature - where a CDS seller can potentially lose enormous amounts of money rapidly if shit goes bad - is practically unique to CDS in Planet Swap - normal swaps don't usually approach their notional amounts nearly in actual cash moving around. CDS actually has payouts approaching the notional value of the swap unlike most swaps.
This is why AIG, an insurance company, went bankrupt: they sold CDS as insurance, and...faced an enormous fucking payout that destroyed them.
CDO/CLO/CMO/MBS/Mortgage tranches - These are often thought of as derivatives even though they don't fit into the forward/option/swap paradigm above. These are all fixed income securities derived from the most basic financial instrument around: the loan.
To a bank, a mortgage (or a loan) is a piece of paper that craps money out every month (when you pay your mortgage). This is extremely lucrative (pieces of paper that crap money out every month tend to be) but even more so when you can sell that money-crapping piece of paper to someone else.
But the other banks don't want to buy an individual mortgage because then they have to know who the money-crapping home-buyer is and that takes time and time is money. So instead, the bank (the structure is more complicated) takes a pile of mortgages and "pools" them - instead of Local Bank #1 selling J.P. Nobody's mortgage, they take, say, a thousand mortgages and put it together in a single bond - the holder gets a slice of whatever those thousand mortgages pay. That way the bank doesn't have to investigate every single mortgage-buyer, they just have to understand the overall mortgage pool.
This pool has unusual features: the mortgage pool has a fixed rate of return if the mortgage holders are solvent. If the mortgage holders go under, the banks foreclose on their houses (and the interest stops coming in).
Banks came up with an idea called tranches, which I think is just French for slices: take a mortgage pool that returns 5% a year (normally) and divide those returns up into separate instruments: one guy gets 2% first, then the next guy gets everything left. Normally, The Next Guy will do very well, but if the pool crashes (everyone starts foreclosing) then The Next Guy might be left with nothing because The One Guy gets his 2% first.
They have complicated terms for this like "equity" and "mezzanine" tranches but the idea is "someone pays less to get fucked first".
There are mathematical ways of modeling the probability of default (bankruptcy) and correlations between bankruptcies (copula). These were fundamental to the valuation of these securities but failed to understand rising correlations and tail risk. In my opinion - but I'm just a history major.
The evil part of this is that it's very easy (in 2008 at least) to take a bunch of mortgages, tranche it like this, and sell off the top few tranches and say "It's as good as treasury bonds!" But these tranches are not very transparent - and when suddenly the market dived...the upper tranches crashed beyond all expectations.
That last paragraph explains the financial crisis in its totality.