A referral program is a system where a company rewards you for bringing new customers. For example, if you tell your friend about an app and they sign up with your code, both of you can get bonuses. It is basically a word-of-mouthed marketing in which rewards are attached.
Companies like it because it enhances their user base, and customers like it because they get free cash, credit or discount. Have you ever signed up for something through referral?