If you have canonicalization errors on your site, visitors will be able to reach your website from multiple URLs such as the www version and the non-www.
This creates a huge problem with the search engines, as you will have two similar pages with the exact same content, which will look like duplicate content.
This could cause your website to drop in its ranking and be penalized by Google.
You will also lose some hard earned link-juice as some backlinks will go to one version and other backlinks will go to the other version.
Tell Google Which Version You Prefer
If you have a Google account you can tell Google if you prefer the www version or the version without the www in front of your domain name.
All you need to do is to go to your Webmaster Tools and then choose the settings option under "Configuration". Here you will be able to select which version you want as your main site.
You may have to confirm that you are the owner of both websites.
When You Link
When you are generating your own backlinks, you need to be very consistent in your linking to be sure that your backlinks go to the same site. Stick to one version when you link to your site and do not switch between the two versions. This will help you correct the canonicalization problem and direct the backlinks to the right website URL.
Of course you have no control over how other people are linking to your site and therefore your backlinks will always be shared between the two sites, though by telling Google which version you prefer, your backlinks will go to the right site.
Make sure that you do not have any canonicalization problems with your site if you want your SEO work to be worthwhile.
Search for your website using both version and see if your site appears under both names. If it does, you need to fix the problem before your ranking drops.