Affiliate Marketing, in its most simplistic description can be explained like this: 

An affiliate tracking software gets hooked up to the merchant’s shopping cart. Then, the affiliate manager finds other websites and newsletters with people who would be interested in the merchant’s products. Those other websites run ads/links advertising the merchant. When a consumer clicks the link, they go to the merchant’s website.

If the consumer makes a purchase, then the tracking software notes it. The affiliate earns a percentage of the sale for every sale they bring the merchant. So, it’s simply a virtual sales force for the merchant’s business.