What is a backlink? It is simply one web site linking to another web site. That link is counted as a backlink to the receiving web site. Google loves to see and count backlinks (although the search engine is NOT interested in sharing its backlink counts with anyone!) and the reason Google loves backlinks is because its the best measure of a sites relevance to a particular topic.

Every link has what is called an anchor text the clickable text of the link and when this anchor text is related to the topic of the target website – that is a vote in Googles mind for the relevancy of the target web site. For example:
A link to a guitar web site has the anchor text of electric guitars that is a great link for the guitar site, because it represents another web site linking to the guitar site with a contextually relevant link. In other words the more links you can get pointing to your web site with contextually relevant anchor texts, the better.

Google sees this as a vote for your web site a sign that your site is truly about guitars. Other sites may link to you with links like guitar accessories or guitar music all of those would be good, too.
Some experts say its not a bad idea to link out to some sites that are relevant to yours, as well. It shows that your site is participating in the niche you are operating in building trust, authority and is a measure of your sites quality. Linking to other sites also often gives you the added bonus of them linking back to you! At the same time, other SEO experts tell you to limit outbound links that it dilutes your Pagerank (one of Googles measures of site strength).

The key is relevancy are the links that are pointing to and from your site making your site more relevant for a user searching the web? Have you ever noticed that Google often ranks non-profit, altruistic web sites higher than their commercial counterparts? Why do you think this is so? I believe the answer lies in the natural link pattern that many non-commercial web sites have they willingly link to other groups and sites sites that may actually be in direct competition with them over an idea or cause. That builds trust and authority in Googles eyes, and may be a good lesson for commercial sites.
The debate on backlinks and their importance will rage on as long as Google keeps their web site ranking algorithm a secret. But its clear that links inbound and outbound are important and really do affect your rankings in the search engines.