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

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 backup files older than a certain number of days.

From MSDN Back Up Database Task (Maintenance Plan)

Backup set will expire

Specify when the backup set can be overwritten by another backup set.

So, there's no deleting of old backups, just overwriting with new ones.

Any advice on how to use "Backup set will Expire:" options while creating Maintenance plan will be appreciated.

This depends on how long you want to keep your old backups. Does your company have a policy for that? Do you move your backups to a storage after a while? If you do, you can specify any number of days for expiry, as long as you copy the backups before the expiry time comes.