The Tag Profile Page in SharePoint 2010 is used by the Managed Metadata Service (MMS) as a landing page for a term or a keyword. It is used to describe the tag, its location in the taxonomy, synonyms etc. It also contains all the latest tagged items and a note board.
The page is quite dull out of the box. Fortunately this page is a Web Part Page and can be customized as you like! You can add Web Parts and rearrange the page. There is not much you can do with the Tag Profile Web Part, but you can edit the Tagged Items Web Part and change how many days it should go back to look for tagged items (default 60 days). The Get Connected Web Part can be slightly configured with what links it will show, see image to the right. And the Noteboard Web Part also has some configuration options such as how many notes to show etc.