Cite
 
biff: /bif/, vt.

[now rare] To notify someone of incoming mail. From the BSD utility biff(1), which was in turn named after a friendly dog who used to chase frisbees in the halls at UCB while 4.2BSD was in development. There was a legend that it had a habit of barking whenever the mailman came, but the author of biff says this is not true. No relation to B1FF.