If you select this option, cloudHQ will replicate sharing metadata (if possible). In other words, if you sync two cloud accounts, and you shared a folder in one cloud account, cloudHQ will share that folder also to the other synced cloud service.

For example, let’s suppose you have a sync pair like this:

Google Drive/Folder_X -> Box/Folder_Y

If the option “Replicate sharing meta-data for files I own” is enabled, and you share a folder Folder_X/ in Google Drive with user alice@company.com, cloudHQ will also share the same folder in Box, so folder Folder_Y/ will be also shared with user alice@company.com in Box.

Replication of permissions in this example will work if you have cloudHQ appropriately configured on your Office365 and Box domain.

NOTE: The detailed instructions on how to do migrate Box to Office 365 is explained here.
NOTE: How to ensure Office 365 OneDrive has impersonation configured is explained here.