Largely misunderstood. Forex, or foreign exchange market, is a global decentralized market for the trading of currencies. The main participants in this market are the larger international banks.
Put simply, affiliate marketing is when you promote a product or service offered by someone else and earn a commission if they make a purchase as a result. In a Forex context, that means linking to an external broker's site or trading platform. If one of the people who clicks on your link signs up, you're then paid a commission based on the size of their deposit, or a percentage of the trades they make going forward. These payment structures vary widely, though.
It is possible to make money with affiliate marketing and many people do precisely that. There's a caveat, though. You need to be realistic. Unless you a) run a site with extremely high levels of traffic or b) are willing to put significant effort into making the venture a success, this probably isn't going to take over as your primary source of income. It's more sensible to treat it as a bonus: a promising supplementary income stream that, if done well, can bring a high return on a relatively modest investment of time.