An affiliate program can be run by a site, to help advertise their product or service, and they pay a publisher/site owner a percentage for doing the following: Me or you for example, running a site would place the advertiser ads on our site/s, someone click on a banner on our site for example and is then taken to the advertisers site, depending on the type of ad, say if they purchase a product from the advertiser, once it is verified, you as the publisher get a percentage of the sale. Thats just one example. Advertiser - offering to pay a percentage to you for running their ads. Publisher - Me, you, anyone, who runs their ads and sends them visiting and buying customers. There are affiliate networks, lots of advertisers and publisher brought together through the network.
basically they give you permission to sell thier products or send people to thier sites and reward you with a commission