Equity Derivative
  
A derivative is something that comes as an outgrowth of something else. There's a thing, and then another thing based on that first thing that can only exist because the first thing existed.
Take the 2017 Tom Cruise remake of the The Mummy. The movie was supposed to be the launch of Universal Studios' so-called "Dark Universe" franchise. There was going to be a series of movies in a classic monster "extended universe"...the Invisible Man, Dr. Jekyll/Mr. Hyde, etc.
The Mummy flopped. The Dark Universe died for good (probably). But why did the movie exist at all? Well, it was a double derivative.
The Mummy was a remake of the 1930s movies that made a lot of money for Universal back when train travel was the preferred way to get from California to Florida. It also rebooted the 1990s/early 2000s version of the franchise, also a money maker in its time. And the new Mummy movie was an attempt to recreate the success Marvel had with its Avengers-centered cinematic universe. See? Derivative...
So, on to equity derivatives. These are contracts whose value is based on some underlying equity, like shares in a public company. The category includes things like options and futures contracts.
For instance, shares of FullBodyWrap Corp. are trading at $10 and you think they are ready to jump. But you don't want to buy the stock outright. So, instead, you purchase an option to buy 1,000 shares at $12 a share, which expires a month from now. The option gives you the right (but not the obligation) to buy the stock. If shares of FBW rise above $12, you can exercise the option, flip the stock, and book the profit. if it doesn't, the option just expires.
You can also trade the option itself. Someone else might want to buy that right to purchase FBW shares. The price people would be willing to pay are based on where FBW is trading. An option at $12 is pretty cheap if the stock is stuck at $10. But, if the stock rises to $15 a share, the price for that option is going to jump significantly. The value of the option is based on the value of the underlying equity. That's an equity derivative.