In Lilo & Stitch, Jumba drives this ship with his partner (and later best friend and roommate) Pleakley during their mission to capture Experiment 626. During the climax when Lilo is accidentally kidnapped by Gantu, Stitch uses Jumba's ship to follow Gantu's ship at the mountains and volcanoes and manages to save Lilo. This ship remains on Earth when Jumba and Pleakley become stranded, and are both forbidden to go back to their home planets under the orders of the Grand Councilwoman.
In Stitch! The Movie, after Jumba is kidnapped by Gantu, Lilo and Stitch drive Jumba's ship to chase Gantu into outer space and engage him in battle, before being defeated and falling back towards Earth.
Jumba's ship is later seen in many episodes of Lilo & Stitch: The Series. In "The Asteroid", Lilo, Stitch, Jumba, Pleakley, and a few of Stitch's cousins drive this ship into outer space to destroy an approaching asteroid to save Earth. In "Shoe", this ship is turned into "Jumba & Pleakley's Bed & Not Breakfast" hotel with the help of Stitch and several other experiments.
In Leroy & Stitch, after Lilo and Stitch had successfully captured all 625 of Jumba's genetic experiments and turned them from bad to good, Jumba and Pleakley were finally allowed to go back to their home planets, and Stitch was given a new job as captain of the BRB. At first, the three choose to stay with Lilo, so as not to hurt her feelings, but Lilo eventually lets them go. Before they drive away in Jumba's ship, Lilo gives them each a present: an Elvis record for Jumba, a rock for Pleakley, and a tiki necklace for Stitch. However, the three eventually become homesick, and in the end, they drive back to Earth to become part of Lilo's ohana once again.
The spaceship was actually created late in development due to the September 11, 2001 terrorist attack incident. Originally, when Gantu accidentally captures Lilo near the end of the film, and Stitch manages to escape to warn Jumba, Pleakley and Nani about Lilo's kidnapping, the four were actually going to steal a 747 passenger jet flying for Tsunami Airlines at Lihue Airport and use it to chase Gantu down the city of Honolulu, the capital of Hawaii, destroying many skyscrapers in the process. However, since the Twin Towers of the World Trade Center in New York City, NY were both destroyed on 9/11 by hijacked airplanes that day, the entire scene had to be reanimated so that the airplane would be replace with Jumba's own ship (it's extremely noticable judging by the shape of the doors and the overall fuselage), and the city of Honolulu was replaced by the mountains of the Big Island of Hawaii (leading to Stitch managing to catch up with Gantu by launching himself out of a volcano). A similar treatment was done to the scene where Jumba and Pleakley raid the Pelekai residence to capture Stitch only to end up accidentally having the house burned down in the process.
Another reason for the creation of this vehicle is to also resolve a potential plot hole likely created by the above in order to show how exactly Jumba and Pleakley made it to Earth in the first place.