Simply put, referral marketing is spreading the word about a product or service through a business' existing customers, rather than traditional advertising.
Word-of-mouth marketing, which occurs when others tell each other about a business, is also considered a form of referral marketing. Word-of-mouth is the principle behind things that “go viral,” like the Old Spice commercials featuring Isaiah Mustafa that were originally released on YouTube. This tongue-in-cheek campaign, with the tag line “The man your man could smell like,” became the fastest growing online viral campaign ever, with 23 million views in 36 hours—and generated a sales increase of 107% for Old Spice. (See also Word-of-Mouth Marketing)
Referral marketing produces the same effect, but is initiated and directed by a business. There's usually some form of incentive or reward offered for customers to refer other people. For example, DIRECTV customers who refer a friend that signs up for their service receive $100 in bill credit—and the newly referred customer also receives a $100 credit.