We haven't seen exactly how this will work yet, but it's probably not dissimilar to what Dropbox did with its Microsoft partnership. Dropbox's iOS and Android apps are tightly integrated with Word, Excel and Powerpoint, letting you create new files in Dropbox and then jumping right into Office to take care of the details. Similarly, your Dropbox storage can be linked to an Office online account. If we had to guess, Google's document types will simply be added to the Dropbox interfaces when you ask it to create new files, presuming you've linked your Google and Dropbox accounts.
Those files will be stored in Dropbox storage, and users will be able to open and edit them straight through Dropbox's interface. Finally, for businesses taking advantage of this, Google Docs files stored in Dropbox will be managed the same as anything else; administrators will be able to revoke access or otherwise keep an eye on those files the same as anything else stored in a company Dropbox account.
Dropbox is integrating with Google's tools in a few other ways, as well. First, a Dropbox for Gmail add-on will let users generate links to Dropbox files right in the Gmail interface. And a tool for the just-announced Hangouts Chat will bring Dropbox files right into the new messaging program -- users can search, share and preview files without leaving the Hangouts Chat UI.
Despite the fact that Dropbox and Google compete in very similar areas, the partnership makes sense on some levels. Increasing numbers of companies are using G Suite for their business work, which means more and more Google documents are floating around out there. At the same time, lots of business are using Dropbox to manage their files as well as for team collaboration. Making those two worlds play better together will benefit users of both platforms, and Dropbox has long said it wants to work with all the tools people use to get things done. Adding Google to its list of partners should go a long way towards making that happen. These integrations are currently expected to go live in the second half of 2018.