Cashback literally means 'money back'. If you as a visitor use a publisher's link to buy something from an advertiser, the publisher gives you a discount or money back (Cashback). The idea is that the publisher gets a commission, because you as a consumer buy something from the advertiser through his link. The publisher gives part of his commission back to the consumer.
So it costs an advertiser nothing more to be promoted by cashback websites. The website itself gives part of its commission back to the consumer. Some cashback websites do not give money but points to the consumer, which can later be redeemed for cash or gifts. There are also initiatives where the cashback is not returned to the consumer, but is donated to charity, for example.