The Custom Field Option Synchoniser add-on is using an Active Object table within the JIRA database to store the syncing information.
You will find two tables responsible for the synchronization.
In this table you will find the synchronization configuration for each custom field.
This table is important for incremental synchronization. For example the add-on stores the Id of the option from the external database
EXTERNAL_ID next to the internal JIRA option id
CUSTOM_FIELD_OPTION_ID. This gives the add-on the possibility to match the options again, even if the option was renamed .