Hi there,
Basically, "www." is a subdomain like any other - it's just a subdomain named "www." and happens to be extremely common due largely to tradition and the set-up of most content management systems. Instead of being named "uk." or "en." (like at Wikipedia), "help.", "analytics." (in analytics.moz.com), etc., it's called www.
The screenshot example would be easier to make sense of if you were comparing the domain http://yoursite.com/ and a subdomain like http://blog.yoursite.com/ - the first shows the authority pointing to your domain's root. The second shows only the blog subdomain's authority. This is the same thing, but with "blog" replacing "www".
It looks here like there is a split between how many incoming links you have to the root and the www. That is, links point to both "versions". If you try to load http://www.yoursite.com and http://yoursite.com/, do both pages load with the same content? If so, one either needs to 301 redirect to the other, or you need to place the canonical tag on the version you do not wish to be indexed and well-ranked, pointing to the other.
If you do not do this, Google finds two versions of the same page (or entire site, if ALL your pages load twice, once with www and once without). Both versions have inbound links, so Google doesn't know which one is meant to be the boss. Worst case scenario is that it ranks both versions poorly as a result, so either redirection from the non-preferred version to the preferred version, or canonicalisation, are the way to go.
You can also set your preferred domain in Webmaster Tools under Settings (see screenshot): http://i.imgur.com/sgrvPKo.png
This may be all basic to you, but hopefully it helps explain why there are two sets of numbers between the "root" and the "same" URL with www. attached. Let me know if this isn't clear.
Best,
Jane