Building backlinks to a website is a critical part of SEO. Virtually all the search engines place weight on how many other sites link to a particular site and factor that into their ranking algorithm. The search engines think that if a site has a lot of links pointing at it, it must be considered valuable in some way by a lot of people.
All links are not created equal, however. A link from a site that receives an extreme amount of traffic would be weighed much more heavily than one with a hundred visitors a month. A link from an educational institution or non-profit organization also enjoys more weight as the search engines consider them less likely to be paid for.
Anchor text, or the words in the link itself, affects how important a link is considered as well. Another factor is whether the site with the link is related to the site it links to. For example, a link from a dog walking service to a dog trainer would be given more weight than a link from a local bar to that same dog trainer.