Inbound links, also called backlinks, are extremely important for a good search engine optimization (SEO) rank and placement.  Google in particular gives enormous SEO value to the quality of the back links to your site.

Notice I said quality, not quantity.  What is a quality inbound link?  A quality backlink is defined as a inbound link to your site from a website that is both 1) topically related to your site and 2) also has its own significant quantity of quality back links to it.  Think of each quality back link to your site as a "reputation vote" where the other site is verifying your importance and status by means of the link it is giving you.  To sustain and improve your search engine optimization results you must continuously check, monitor and increase the amount of quality inbound backlinks to your site.