SkyDive Pro in SharePoint 2013 has nothing to do with SkyDrive.com. Do not worry, nothing will go to Microsoft's server or users personal SkyDrive accounts.
SkyDrive Pro, while being your MySite Documents library, is also the name of the technology that syncs SharePoint 2013 to your desktop.
The desktop sync works like original SkyDrive with an entry in favorites of windows explorer. You can have multiple libraries synced to your desktop (now drag and drop documents).