Back Links are link to your website from another website. If your page has more backlinks then your page has better pagerank. It indicates us how popular website is.
One easy way to increase your backlink count is while posting in other blog, leave you website link with Dofollow attribute.
BacklinkWatch is an online free site where you can check backlinks to your website.
Go to www.backlinkwatch.com and type your website address and click submit button. You will get the link of websites where your backlink is posted.