A lot of Rome is built on top of Microsoft's Xbox SmartGlass technology. SmartGlass, introduced with Windows 8, allowed devices, including TVs, to "talk to each other" enabling users to get supplemental information on TV shows, movies, music, sports and games on a second screen.
With Rome, Microsoft added an App2App contract layer for applications and services. This app-to-app communication layer is new as of Windows 10.
Rome "enables users to connect, manage and control any connected app or device proximally or from the cloud," Microsoft execs told Build attendees. Rome exposes users' device graphs, so that apps can discover other apps on a variety of devices via Bluetooth, local networks or the cloud. In addition to finding other eligible apps and devices with which to connect,
Rome also includes a new programming interface that ensures that links open in mobile apps, rather than on the Web, when possible. After launching an app, Rome provides the messaging between apps, as well as app handover and/or remote access when users are moving from one device to another but continuing with a certain task.
Microsoft officials said they would make Project Rome available to developers as a WinRT programming interface as part of an upcoming Windows 10 Insider software development kit. (I don't believe Rome is part of the Anniversary Update SDK announced last week, but if anyone knows otherwise, let me know.)
Microsoft also plans to release software development kits for iOS and Android devices, enabling Rome to work beyond just the Windows ecosystem later this summer.
"Windows Task Continuity" is codenamed "OceanView" (another Microsoft codename unearthed by The Walking Cat), for what it's worth. So perhaps the overall Windows 10 app-handoff scenario is OceanView, while the specific hand-off APIs enabling it are "Rome"? (If anyone knows for sure, chime in.)