A back link is a link on a any site that links back to your site. Google sees back links as a vote for your site. Google assumes people will only link to sites that they find useful.
Keep in mind not all back links are treated the same. For instance if a family member has their own website and links to you it won't do much good. However, if a site like CNET or CNN links to your site you will get a huge boost. You also need to be sure the pages that link to you are relevant to your site.
You should also be aware of do-follow and no-follow links. Many popular sites will turn all outgoing links into no-follow links. A no-follow link doesn't do you any good when it comes to search results.
If you are thinking about doing some back linking, its a good idea to join forum sites that have high PR Google ratings that are also relevant to what you are linking to. However, before you start adding links its a good idea to get involved with the forum community on the site by posting a few posts that add value to the site. Later you can start adding your link in your post, but be careful not to SPAM the site. Their is a fine line between posting a helpful link and SPAM.
Basically, the more relevant back links that you have the more Google will like you.