"Forex" stands for foreign exchange and refers to the buying or selling of one currency in exchange for another. It's the most heavily traded market in the world because people, businesses, and countries all participate in it, and it's an easy market to get into without much capital. When you go on a trip and convert your U.S. dollars for euros, you're participating in the global foreign exchange market.
Forex is a portmanteau of foreign currency and exchange. Foreign exchange is the process of changing one currency into another currency for a variety of reasons, usually for commerce, trading, or tourism. According to a recent triennial report from the Bank for International Settlements (a global bank for national central banks), the average was more than $5.1 trillion in daily forex trading volume.