In an affiliate marketing program, the "affiliates" put up links on their own sites that drive traffic to merchants. They're useful for both content- and sales-driven sites, and you can join them as either a merchant or as an affiliate — it just depends on what you think will be most valuable and fitting for your business.
Affiliate programs generally pay out in one of three ways. Pay-per-sale programs pay the affiliate only if a visitor makes a purchase on the merchant site. Pay-per-click programs, which make the most sense for content-driven sites, pay the affiliate for each time someone visits the merchant's site by clicking on the affiliate's link. It doesn't matter what the visitor does once they're on the merchant site. In a pay-per-lead program, the affiliate gets paid only if the visitor fills out an email sign-up form on the merchant site.
You can probably imagine that it's a lot of work to run your own affiliate program as a merchant. That's where handy-dandy affiliate networks come in. The network acts as a middleman, taking care of traffic monitoring, link setup, recruitment and payment. They'll also take a cut of each transaction, but many businesses find it's a small price to pay for the convenience.