When you select Dropbox as your storage mechanism in draw.io the next splash screen will be
Click the Authorize button to allow draw.io to access a specific folder in your Dropbox, usually Apps/drawio. If you want draw.io to forget your Drobox authorization later on, when logged in your name appears in the top right pull down
Selecting Sign Out will de-authorize your current login to Dropbox (it won't disconnect the application from your Dropbox permanently).
Dropbox permissions and privacy
The first time you authorize Dropbox you will see a dialog like
When you click Allow draw.io will have write and read permissions to only that folder. This means that all your files not related to your diagrams are completely secure from draw.io.
Linking draw.io to Dropbox means that draw.io can read basic information about you, including your email. However, none of this information resides anywhere except your browser and Dropbox's server, it is never passed up to draw.io servers.
Changing your storage settings
Once you are authorized you'll see the new/open dialog. See the Starting draw.io section for a description of how to use this.
If you decide to switch default storage mechanism at any later point, navigate to the application web page and you'll see this dialog. Click on Not using Dropbox and your storage selection will be forgotten and the initial storage splash displayed. If you want to change Dropbox user logout use the pull down menu on the top right.