A forex or currency futures contract is an agreement between two parties to deliver a set amount of currency at a set date, called the expiry, in the future. Futures contracts are traded on an exchange for set values of currency and with set expiry dates. Unlike a forward, the terms of a futures contract are non-negotiable. A profit is made on the difference between the prices the contract was bought and sold at. Most speculators don't hold futures contracts until expiration, as that would require they deliver/settle the currency the contract represents. Instead, speculators buy and sell the contracts prior to expiration, realizing their profits or losses on their transactions.
The foreign exchange market is where currencies are traded. Currencies are important to most people around the world, whether they realize it or not, because currencies need to be exchanged in order to conduct foreign trade and business. If you are living in the U.S. and want to buy cheese from France, either you or the company that you buy the cheese from has to pay the French for the cheese in euros (EUR). This means that the U.S. importer would have to exchange the equivalent value of U.S. dollars (USD) into euros. The same goes for traveling. A French tourist in Egypt can't pay in euros to see the pyramids because it's not the locally accepted currency. As such, the tourist has to exchange the euros for the local currency, in this case the Egyptian pound, at the current exchange rate.