What is traded on the Foreign Exchange?

The simple answer is money. Forex trading is the simultaneous buying of one currency and the selling of another. Currencies are traded through a broker or dealer, and are traded in pairs; for example, the Euro dollar and the US dollar (EUR/USD) or the British pound and the Japanese Yen (GBP/JPY).
Because you're not buying anything physical, this kind of trading can be confusing. Think of buying a currency as buying a share in a particularcountry. When you buy, say, Japanese Yen, you are in effect buying a share in the Japanese economy, as the price of the currency is a direct reflection of what the market thinks about the current and future health of the Japanese economy.
In general, the exchange rate of a currency versus other currencies is a reflection of the condition of that country's economy, compared to the other countries' economies.