Backlinks serve several purposes.
1)They have the potential to direct traffic from the linking website or page, assuming there are people there to follow the link.
2)The search engines consider backlinks to be a "vote" for the site or page in which they are linking.
3)Since search engines rank pages/sites based upon factors, including the number/quality of backlinks, the page/site will rank higher on the Search Engine Results Pages (SERPs). By being highly ranked for various specific search terms, you could see a great deal of traffic. Search Engines are typically the best source of traffic.