A derivative is a contract that 'derives' its value from the performance of an underlying asset sometime in the future. A bitcoin derivatives market is where you can buy or sell bitcoin futures contracts if you are confident in which direction the bitcoin markets will move. Most derivatives have a settlement date on which all contracts are finalized and your position is liquidated. Bitcoin derivative markets allow traders to leverage their position and make a profit whether the price of bitcoin goes up or down.

In a 'Long' position you are borrowing fiat currency such as USD to buy bitcoin with a goal of selling that bitcoin at a higher price.

In a 'Short' position you are borrowing bitcoins to sell for a fiat currencies with the goal of buying bitcoins back at a lower price.

When your trade ends the loan is repaid and you keep all the profits.