Back links are the links that are directed to your site from other sites. The number of incoming links is an indicator of your site's popularity. You can consider each incoming link as a vote for your site. The more votes that you have from reputable sites the higher your PageRank. As pages are ranked separately links within a site also play a part in the PageRank. For a long time PageRank (one word) was thought to be the main consideration in the page ranking by the search engines. This is no longer the case, although it does figure into the search engines Algorthm. PageRank only covers links it is not the overall rank of the page
Regardless of the search engines its always good to have reputable sites link back to you its provides another way for users to find you.
Check Your Back Links
You can check the links back to your site:
Yahoo - type in the search box
linkdomain:http://the domain name
From Yahoo you will also get the links for your own site you need to select "exempt from this domain" it is in the show inlinks in the drop-down menu at the top of the page
Google - type in the search box
link:http://the domain name