The clue is in the name - Rome is a homophone of roam.

"Project Rome allows developers to write apps that can run on multiple devices and travel with the user as they switch between devices." [0]

So it's allowing a programmer to sync and script behaviours from Android/iOS phone to Windows desktop to xbox etc using a MS login.

I would assume it's the technology behind the Your Phone Companion app that sends an SMS from a connected PC.

[0] https://docs.microsoft.com/en-us/windows/project-rome/