Backup set expire option - Backup SQL Server 2012
Answered here by @JamesAnderson

The "Backup set will Expire" option is used to indicate how long a backup should be prohibited from being over written. It will not clean up old backup files. You can use the "Maintenance Clean up Task" in your maintenance plan to clean up backups files older than a certain number of days. 

What is the use of &quot;Backup set will Expire:&quot; option while creating Backup Database task in Maintenance plan