This is a kind of cool web part. It’s cool because it allows you to have a "Favorites" list within your team site that is collapsible, can be grouped under categories and then categories can be relocated using drag & drop – and the UI for laying out the information is a lot more intuitive than the standard list presentation page.
It’s only "Kind of" because it does not have an associated list driving the content like a standard links list does. You could build your own, but then the layout UI is not as user friendly.
I see this web part being used mainly in My Sites… but then if you are using a browser to access the site, and you are keeping a list of links that are useful to you in your my site, where is the benefit over the "Links" bar in IE?
Anyhoo, at least y’all know it’s there.