What is traded at the Foreign Exchange?

Of course, Money.

Forex trading is the buying of one currency and the selling of another. Currencies are traded in pairs, for example EUR/USD, USD/JPY, EUR/GBP etc. Currencies can be traded through a broker or dealer. So if a trader believes that Euro will gain against the Dollar, he will sell Dollars and buy Euros.

As you're not buying anything physical, this kind of trade can be confusing to you. You could just imagine that buying currency as buying a share in that country. When you buy the Dollar, you can think of it as you are buying a share in the US economy and if the US economy is doing well, the Dollar will rise and you will gain when you sell the Dollar later. The value of curriencies are direct reflection of the state of economy of the respective countries.