That's the SQL transaction log for your backup exec database. I suspect you'd have a hard time deleting even if you wanted to, since it's always going to be locked, but even so I wouldn't recommend it.
Basically the file stores a record of every change which is made to the BEDB database, until such time as a full backup of the database is run, the old changes are committed, and are removed from the file. One thing to note however is that it's possible that most of that 13 gig is empty space, as unless SQL is specifically told to do so it won't strink the database. How to check this is to open Enterprise Manager, navigate to the BEDB database in the left hand pane, right click on it and select View, Taskpad. You'll then see a load of information about the database near the bottom of the page in the right hand pane.
From a SQL perspective one thing you could do would be to go into the properties of the BEDB database, go to the Options tab, and change the Recovery Model to Simple. That will then mean that changes are just made to the database, rather than being recovered in the transaction log, though it will then remove the possibility of going back to a specific transaction in the event of a restore, but that might not be an issue for you. What I don't know is if that will have an adverse effect on Backup Exec.
