When Google was first developed its founders were seeking a way to make search more relevant. They noticed that searches for the US president at the time, Bill Clinton often returned irrelevant results. Some results were of general low quality (e.g. a "Bill Clinton joke of the day") while other results that users would consider relevant were missing (for instance, the main site for the president, whitehouse.gov).
Their conclusion was that links and anchor text could both be used to solve this problem:
The initial concept was based on the idea that academic papers typically cite related and influential works, and that links can be regarded as very similar to such citations. Working out how valuable an individual link is and giving it a score (called PageRank) allows a search engine to identify the most important pages:
Academic citation literature has been applied to the web, largely by counting citations or backlinks to a given page. This gives some approximation of a page's importance or quality. PageRank extends this idea by not counting links from all pages equally, and by normalizing by the number of links on a page.