Even if you continue to host your data on Dropbox or Google Drive, you have total control over the underlying data--you can audit, modify, or delete it at any time.

From the application side, it also means you no longer have to deal with persistent state, which means you can ship applications with no backend. That's an order of magnitude easier to develop and maintain.

The downsides are real though: the user experience is often jankier, and the lack of a central database makes it really hard to do anything social/realtime. I'm rooting for Solid but am not yet convinced they'll make it.