You shouldn't expect many visible changes in a .x update to an established program, and while there are some exceptions to that rule, iTunes 12.1 isn't one of them.
Perhaps the most important change in iTunes 12.1 is improved synchronisation with iOS devices - and that should be a welcome change for iPhone, iPad and iPod touch owners suffering from poor performance in this aspect of the program.
There's also a cosmetic/UI change in the Info window: fields are now shown with a surrounding box, making it obvious that the contents are editable.
When listening to iTunes Radio, the widget also displays a price button which, when clicked, purchases and downloads the current track.
The problem is that according to user reports, this is a 'one-click' purchase. If you are logged into the iTunes Store through iTunes (and presumably have entered your password sufficiently recently), clicking the button is said to complete the purchase with no further interaction.
In other circumstances, the need to enter the password for the AppleID associated with the iTunes Store account provides an opportunity to reconsider
iTunes 12.1 requires OS X Lion or later (some reports have erroneously stated it is only for Mavericks and Yosemite).
The Notification widget is apparently only available in Yosemite, and reportedly requires manual activation via Notification Center or the Extensions system preference.
iTunes 12.1 is available for download here. Existing iTunes installations can be updated to version 12.1 via the Updates tab of the Mac App Store, by selecting Software Update from the Apple menu, or the Check for Updates command in the iTunes menu.
The ability to purchase the currently playing iTunes Radio track is included in the main window of iTunes 12.0.