You'll notice at the bottom of the preferences page a list of subscriptions and a link to a directory of subscriptions. Each Subscribed Link matches some of your queries (for example, queries about weather, nutrition, traffic) and shows information extracted from a database. It's like a Google OneBox created by third-parties, but you can decide if you want to see it and there's always an option to unsubscribe.
According to the FAQ, "using Subscribed Links, you can add information created by providers you trust to your Google search results pages. Whenever you search on Google in an area of their expertise, you'll see a custom result from those providers in your search results. (...) Your Subscribed Links will appear in the fourth search result position", even if they aren't counted as a real search result.
Here's what happens if I subscribe to the Nutrition Facts knowledge source and search for [calories in cream of celery] or even [cream of celery]:
Even if other results offer similar information, I get the benefit to find what I want without having to click on a search result. In some cases, it's not necessary to enter the context of my search because my subscriptions already provide that context ([cream of celery] shows information about calories because I'm interested in nutrition).
The Subscribed Links are some special search results with custom snippets and a limited range of queries that are displayed based on your preferences. They allow you to perform specialized searches on a general-purpose search site.
And if you're not satisfied with the limited number of Subscribed Links that are available, you can create one and promote it on your site.