Each and every folder added to Sync is associated with a database containing all the information about the folder and its contents. Database files are located in Sync's storage folder.
If this error appears right after you add the folder, most likely Sync was not even able to create database due to lack of write permissions in storage folder, recheck that in first place.
If the error appears in the course of using Sync, a data fragment from the DB file gets corrupt and can’t be read properly, the database driver fails to provide access to the data source and thus database error pops up. To avoid incorrect file updates, Sync will suspend synchronization of the folder whose DB is corrupted, whereas the rest of the folders should continue syncing as before.
This problem may be caused by Sync shutting down incorrectly which, in its turn, can be the result of a system/application crash or an improper/forced shutdown:
1) Try quitting and then restarting Sync.
2) Re-add the shared folder to Sync (prior to that, be sure to disconnect and remove the folder from the program).
Another possible cause might be a damaged disk sector, virus, or some other s/w that might be accessing the files. Run disk check, antivirus scan.
If this error persists, please, send debug logs to support team though "Help -> Contact Support" menu in Sync app, or collect debug logs manually from peers affected and send them though the web form.