Affiliate marketing allows you to recommend products and services from other companies and be paid a commission if someone buys the product as the result of your recommendation. To track which purchases happens as a result of your recommendation(s), the merchant will provide you with a special link to use when linking to their website that contains a unique referral code assigned to you. If people click that unique link, and buy the product or service within a specified timeframe (the timeframe varies depending on the merchant), you get a commission on the sale.
The problem with affiliate marketing, like many other home business options, are the so-called gurus and get-rich-quick programs that suggest affiliate marketing can be done fast and with little effort. Odds are you've read claims of affiliate marketing programs that say you can make hundreds of thousands of dollars a month doing almost nothing ("Three clicks to rich!"). Or, they suggest you can set up your affiliate site, and then forget it, except to check your bank deposits.