FOREX stands for foreign exchange, the buying and selling of world currencies. You might use your dollars to buy Japanese Yen, for example. Or use your Great Britain Pounds to buy Mexican Pesos. Or any such pair of legal tender currencies. When you travel abroad and exchange your money for the local currency, that is a FOREX trade.
The value of the world’s various currencies goes up and down, and FOREX traders hope to make a profit from this movement. For example, if I believe that the Euro will go up in value in relation to the dollar, then I might use some dollars to buy Euros and see if the value goes up. Then if I trade back to my dollars I might have more than I started with, my profit. In the past, FOREX trading was limited to professionals at financial institutions, but it has become more available to the average person with the advent of online trading.