An backlink is a link pointing to a page on a website from a different site. People use the term "backlink" when they're looking at the link from the point of view of the site that's linked to. Backlinks are also referred to as inbound links as well.
Backlinks have usually been thought of as the most important ranking factor that helps a site appear higher in search results.
With backlinks, quantity and quality matter. For example, to achieve the same SEO benefits from backlinks you could get a few really backlinks from authoritative web pages with high PageRank, or many links from less authoritative web pages.
For more information, and for tips on getting quality backlinks, read our articles about link building.