Compare Rows will go through and see which sys_ids exist in the local instance but do not exist in the target instance and vice versa. Because some tables can be rather large, this feature will run in the background as a scheduled job and the Compare Rows Status field will show the status from when the job is scheduled (after clicking Compare Rows to start it) to when it is running in the background to completed when it has finished processing all the rows of the table both on the local instance and the target instance.
The Compare Rows Started and Compare Rows Completed fields will provide the date and time when the scheduled job starts and completes. You will need to reload this form in order to see changes in the Compare Rows fields with its results and as mentioned for large tables, it is recommend you check back later to give it to time to run the comparison (for example, a test of 150,000 records took about 25 minutes to complete).
For cases where there are discrepancies the Compare Rows Status field will show a status of Completed with Discrepancies and the records that are missing in either instance will be listed in the PSP Row Discrepancies table found at the bottom of the page. For those sys_ids that exist in the local instance and do not exist in the target instance, the sys_id will be listed with a state of Missing in target. The sys_ids that do not exist in the local instance but exist in the target instance will be listed with a state of Missing locally.
Once you have this list of sys_ids at the bottom, you can then research why these sys_ids are missing and handle appropriately, including manually exporting the XML of a missing record from one instance and importing the XML into another instance, running DataSync bulk share on the missing sys_ids, etc.
NOTE: In order to improve performance when the Table Compare feature is accessing the PSP Row Discrepancies table, a daily background job will run against the table to delete records that are older than a week and show as Record Imported as well as delete all records older than a month.