The Arquilian Galaxy is a tiny galaxy held by the Arquilians. According to Frank the Pug, the galaxy is the best source of subatomic energy in the universe, 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 point of origin, 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 mortally injures an Arquilian, the latter's final words are, "To prevent war, the galaxy lies on Orion's Belt", which nobody can figure out, as Orion's Belt is a series of three stars, not nearly the billions needed. It is not until they speak with Frank 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.