aCalendar is generally not involved in calendar synchronization, but displays error codes and error messages from the sync adapter, which handles synchronization between cloud and Android.
For tasks, aCalendar does provide synchronization for Google Tasks and MS Todo. CalDAV Tasks configured via Open Tasks, are synchronized by external sync adapters, e.g. davX5.
Android error messages
The Android system predefines several error messages for common problems:
already-in-progress, this can usually be ignored, it is shown when another sync request is issues while sync is still running
authentication-error, this usually means, that the credentials are no longer valid, e.g. because a password was changed or permissions were removed. Usually the responsible app should ask for your credentials or consent again. Otherwise, try re-adding the account
io-error, this can be any network-related problem (io stands for input/output). Check the internet connection and/or try later.
parse-error, a server message was in an unexpected format. Try again later, or if this doesn't help, re-add the account.
too-many-deletions, some sync adapters limit the number of items to be deleted at once to avoid accidental mass-deletion of your data. The sync adapter should prompt you to confirm or undo the deletions. If you are not prompted for this, check if the sync adapter app has notification permissions.
internal-error, this can be any internal problem within the sync adapter. Try again later, or if this doesn't help, re-add the account.
Known sync-adapter-specific error codes
Sync Error 6 (Samsung Active Sync/Exchange Sync), some versions of the Samsung Active Sync adapter fail to edit/create any event with an Outlook category set. You must remove any Outlook category before editing the event. Removing the category after the sync error shows does not fix the event's sync status.