It's a reference to the movie Steel Magnolias. The groom's aunt made a red velvet cake in the shape of an armadillo, and covered it in grey icing. When you cut into it, it looked like the insides of a creature. It was kinda gross looking.
When the father of the bride (who was annoying the aunt of the groom) asked for a piece of cake, she hacked off the tail of the armadillo and gave it to him. He just smiled and said "I always did like a nice piece of tail."
Steel Magnolias is a fun movie, but a real tear jerker. It stars Julia Roberts(the bride), Sally Fields (mother of the bride), Dolly Parton, Olympia Dukakis, Shirley MacLaine, and Daryl Hannah. Tom Skerrit plays the father of the bride and Dylan McDermott is the groom.
LOL! That sounds like something out of Peter Jackson's early movie Bad Taste :)
BTW, speaking of Olympia Dukakis, I always wondered, is she related to Michael Dukakis or not?