What exactly does CalDAV-Sync do? Android has this Bug, that prevents you from using a standard CalDAV application.

This App corrects that bug:


  CalDAV-Sync is a CalDAV client for Android to synchronize events. Due
  to its implementation as sync adapter it integrates seamlessly with
  the native calendar app and widgets.(Also check out CardDAV-Sync)
  
  Important note for Jelly Bean users: To prevent the removal of your
  accounts on reboot install this app:
  https://play.google.com/store/apps/details?id=org.dmfs.jb.workaround.caldavsync
  
  This app will create new calendars on your device (one for each
  calendar on your server account)


How exactly does it solve it?

Is it an alternative synchronisation? Or does it correct the bug?
According to the fix app, the actual bug it fixes is 34880.

Basically, Play installs paid apps to the wrong location, specifically to /mnt/asec instead of /data/app.  When the service cache is generated on boot, that location is not yet mounted, so the service and the associated accounts gets removed.

This works around that by using the same account on a non-paid app, which installs normally, get picked up by the service cache, and this prevents the account from getting removed.