As the name of the option implies, it will allow you to install a given app to any of the Windows 10 devices that are currently associated with your account. So even if you aren't physically in front of the desktop PC in your bonus room, you can actually install an app like Netflix or Amazon Music by logging into the Microsoft Store from a web browser.
It doesn't appear that this feature has rolled out to everyone at the moment, as both of my completely up-to-date Windows 10 machines with the April 2018 Update installed aren't showing the option. However, Bleeping Computer says that clicking on the "Install on my devices" button will bring up a list of all the active machines attached to your Microsoft account. From there, you can hit the "Install now" button to choose your desired machine.
We should note that the app installation doesn't occur immediately. According to Bleeping Computer, it took roughly 15 minutes from the time the installation was initiated until the Netflix app was finally remotely loaded on a test machine.
While it's nice to see that Windows 10 is gaining this feature, Google has offered similar functionality for years via Google Play. In addition, even the Xbox One offers the ability to remotely install apps. The real question, however, is will this function prompt more people to actually use the Microsoft Store for apps.