The derivatives market is the market in which contracts whose value depends on an underlying asset, rate or index are bought and sold. The main contract types are futures, options and swaps such as the interest rate swap. The instruments themselves are explained on the Derivatives page.
Trading happens on exchanges, where a clearing house stands between buyers and sellers, and over the counter (OTC), where two parties deal directly. Crypto has its own derivatives market, led by perpetual futures, which often trades more volume than the spot market.