(written from a Production point of view)
Established in the writers' second draft script of the Star Trek: Enterprise episode "Breaking the Ice", the "Comet Special" was a type of meatball sandwich concocted by Chef aboard Enterprise NX-01. He designed it as an in-joke reference to the fact that the starship was meanwhile studying a rogue comet. The meatballs in the sandwich were meant to represent comets.
In the script, Captain Jonathan Archer showed the sandwich to Commander Trip Tucker. Trip was at first unimpressed by the sandwich, but after Archer explained that the meatballs were intended to represent comets, he responded that the sandwich was "clever."