The WordPress.com desktop app puts WordPress.com in your dock or taskbar. Use it to focus on your content and design with no other browser tabs to distract you, or to keep your sites readily accessible. The app is powered by the same technology that runs WordPress.com.
To edit your self-hosted WordPress (.org) website, you need to install the Jetpack plugin, which you can do by following the instructions here.
Once Jetpack is installed and connected to a WordPress.com account, make sure the Jetpack Manage module is enabled.