For search engines that crawl the web, links are the streets between pages. Using link analysis, the engines can discover how pages are related to other pages and in what ways. Since the late 1990's links have also served as a stand-in for votes - representing the democracy of the web's opinion about what pages are important and popular. (Some refer to this as the reasonable surfer model). The engines themselves have refined the use of link data to a fine art, and incredibly sophisticated algorithms create nuanced evaluations of site and pages based on this information.
Professional SEOs attribute a considerable portion of the search engines' algorithms to link-based factors. Through links, engines analyze the popularity of a site & page based on the number and popularity of pages linking to them, as well as metrics like trust, spam, and authority. Trustworthy sites tend to link to other trusted sites, while spammy sites receive very few links from trusted sources. Authority models, like those postulated in the Hilltop Algorithm, suggest that links are a very good way of identifying expert documents in a given space.
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