Starting with the OneNote for Mac update in the App Store) (version 15.7.1 released on February 17, 2015, we changed the minimum system requirements for OneNote to take advantage of the latest and greatest capabilities in Mac OS X Yosemite (10.10). Yosemite (10.10) is a free upgrade and is supported on the same hardware as Mavericks (10.9).
If you previously installed OneNote for Mac and are on OS X Mavericks (10.9), you can continue using the older version of OneNote for Mac, however in order to get this update or any future OneNote updates, you must upgrade your OS to Yosemite 10.10 or later.