The Arquilian Galaxy is a tiny galaxy held by the Arquilians. The galaxy is a large source of subatomic energy, and because of this, Edgar the Bug comes to Earth to search for it. It can be assumed that the Galaxy is the property of the Arquilians, not their homeworld, as they are over 200x bigger than the Galaxy. They probably use the Galaxy for power.
When Agents J and K learn about this plot, they extensively search for the Bug and the Galaxy. When the Bug nearly kills an Arquilian, whose final words are, "To prevent war, the galaxy lies on Orion's Belt". Nobody can figure it out, as Orion's Belt is a series of three stars, not nearly the billions needed. It is not until they speak with Frank the Pug that they realize that even though it has to be billions of stars, they could be tiny stars. After seeing a cat, J knows that he meant his cat's, Orion, collar. Unfortunately, they are too late, as the Bug has already found it and the Arquilians reveal they will destroy the Earth if it is not obtained, to prevent it from falling into the hands of the Bugs. The Bug eats the marble sized galaxy, and attempts to fly away in a ship. However, J and K shoot the ship down, and after a fight, they finally get the galaxy. In the end of the movie, it is revealed that every galaxy is actually marble-sized, and held by some other aliens, who use them to play marbles.