Mirroring in SQL Server Standard Edition
Check the following system view:

SELECT *
FROM master.sys.database_mirroring;


There is a wealth of information in there about the status of your mirrored databases.

If the column mirroring_state_desc contains 'SYNCHRONIZED' then it is indeed synchronized.

What SYNCHRONIZED indicates is that all outstanding transactions from the master have been successfully committed into the mirror database.

If it shows a status of SYNCHRONIZING then the mirror is "behind" the principal to some degree.

You can also use the Database Mirroring Monitor app to monitor the status of mirrored databases.