You back up the tail of the log when you want the database to be unavailable for further transactions, like when you intend to restore the database in-place.
That is the key difference between a regular transaction log backup and a tail backup: when you back up the tail of the log, the database is put into the recovering state and no further transactions can be performed against it. A regular transaction log backup leaves the database in its operational state.
If you aren't going to restore the database in place, and want the database to remain available for further transactions, you just take a transaction log backup.
See Tail-Log Backups on MSDN