Google links “authority” sites. If many relevant, authoritative, content-rich sites link to yours, it implies you’re important, and therefore worthy of a higher ranking.
With more important sites ranked near the top of search results, web searchers have a better experience, so they continue to use Google, who continues to make money, which makes shareholders happy.
For this reason, your site needs to be neighbor-friendly. It should be designed so that you can link to other sites easily, and there should be an ongoing effort to find relevant sites that will link to yours, preferably with text links, not link pages. This is what we call link building.
But not just any site. Sites considered to be “link farms” with dozens or hundreds of others aren’t helpful to your ranking. Some experts claim that Google will actually penalize your site if you have links to/from these sites. This is not the type of link building I recommend!
Google has increased the influence of what’s known as trust in links. Trust comes from more than just link “count.” A variety of factors influence Google’s trust of a web site. It’s not entirely clear what they are, but an example would be linkage from an .edu site and long-term domain name registration. Some of this can help you avoid the Google Sandbox.
This is why I’m big fan of Yahoo directory and the Open Directory Project. These directories are organized by theme, meaning that a link from there can really give your site a shot in the arm on relevance since they pass some level of page rank.