The main villain in Pokemon Sun and Moon didn't get revealed until very, very late into the game. However, after finally revealing the villain gamers understood how it tied the story all together, and there's some new concept art that delves just a bit deeper into her design.
The concept page shows a numbered list of conceptual designs that go into Lusamine and her special case that was used to keep Nebby locked away. There's a picture that shows Lusamine holding the case close to her, as well as a detailed breakdown of how the case works.
In Pokemon Sun and Moon it was designed to contain the legendary Cosmog, who could either turn into Solgaleo or Lunala. The illustrations show that the box can be used to keep Pokemon contained and when activated the points on the box light-up and glow blue. When it's empty the lights dim and fade to black, matching the color of the rest of the box.
We actually don't see much of the box in the game until near the end, when Lusamine reveals that her goal is to open a wormhole to the Ultra Space world and unleash the Ultra Beasts. The box would presumably be used to capture Ultra Beasts, since normal Poke Balls weren't going to be enough. During the end of the game we see the box in the background in the laboratory of the Aether Paradise isle where Lusamine had Nebby, the Cosmog, captured.
The concept art adds a bit more depth to how Lusamine could have used the box to either capture or unleash Ultra Beasts, which became a central theme in Pokemon Sun and Moon later on in the game.
The Cosmog featured throughout the title was carried around by another central character who was on the run, named Lillie, Lusamine's daughter. At the very start of the game when the guards are chasing Lillie and Cosmog, who she named Nebby, it unleashes its legendary power briefly to help them escape. The box in the concept art appears to show that the Pokemon's power would have been contained within, and only unleashed at the discretion of the wielder. The one image appears to show that it could possibly have been used a portable teleportation device if Cosmog was trapped inside, enabling the wielder to travel back and forth between Ultra Space.