From what I can tell, it is the pointer (or information file) that tells log shipping where it left off with its last restore.  We log ship throughout the day, but only restore the log backups on the secondary database between 2 & 4 a.m.  There is always a .tuf file after the last restore.  I imagine that it contains the FirstLsn and LastLsn of the T-Log backups, but that's just a guess.