Backlinks are links that are directed towards your website. Also knows as Inbound links (IBL's). The number of backlinks is an indication of the popularity or importance of that website. Backlinks are important for SEO because some search engines, especially Google, will give more credit to websites that have a good number of quality backlinks, and consider those websites more relevant than others in their results pages for a search query.
When search engines calculate the relevance of a site to a keyword, they consider the number of QUALITY inbound links to that site. So we should not be satisfied with merely getting inbound links, it is the quality of the inbound link that matters. A search engine considers the content of the sites to determine the QUALITY of a link. When inbound links to your site come from other sites, and those sites have content related to your site, these inbound links are considered more relevant to your site. If inbound links are found on sites with unrelated content, they are considered less relevant. The higher the relevance of inbound links, the greater their quality.