To give a short answer to your question derivatives are things that derive their value from some other underlying thing. The classic example would be options. Stock options are contracts that give you the right (but not the obligation) to buy or sell a certain stock for a certain price until a certain day. They cover 100 shares per option. The right to buy is called a "Call" the right to sell is called a "Put." For example a Sept 21 2018 80 call option for Gilead gives the owner the right to buy 100 shares of GILD for 80 dollars per share any time until Sept 21. The current price for said option is about 2.25 per share or $225 for the option. If the price of Gilead shares goes up a bunch above 80 between now and then the option will make a lot of money. Say by Sep the price of GILD is 90 the option would be worth 10 per share or $1000. If the price of GILD is less than 80 on that date the option would be worthless because why would you buy the right to buy shares for 80 if they are going for less?
TL.DR Derivatives are very volatile ways to make or, more likely, lose a bunch of money really fast.