The Millennium Falcon cargo ship that is one of the most recognisable ships in science fiction and loved. Originally owned by Lando Calrissian who lost it to Han Solo gambling. It is used by Lando to lead the Rebellion assault on the second Death Star, co-piloted by Nien Numb.
It has been described as the fastest ship in the galaxy that can do the Kessel Run in twelve parsecs. In Astronomy talk, a parsec is distance not time and is one of the most well known scientific bloopers. The Solo movie explains the Kessel Run is the shortest distance from the Coaxium fuel depot on Kessel and the outside of the surrounding nebula.
It was the craft that Obi-Wan Kenobi hired to take Luke Skywalker and the droids ( C-3PO and R2-D2 ) to Alderaan unaware at the time that the planet was to be blown up. Even though it was the fastest ship, it was unable to escape from the Death Star's pull which pulled it inside. The Cargo ship had secret compartments where the crew hid from the Stormtroopers that was sent on board to search.
At the Battle of Yavin IV, Han Solo had at first declined to take part in the asssault on the Death Star but some short tme later, he changed his mind and played a pivotal role by blasting Darth Vader TIE Fighter away so that Luke Skywalker could fire the missile that blew up the craft.
Although unlike in other sci-fi when the captain can speak directly with the ship's computer, for Han Solo to do so, Han needs an interface to do so. When C-3PO enquires what Han Solo of him, Han replies he wants C-3PO to talk to the ship. It is revealed in Solo - A Star Wars Story that a robot's personality and memory was uploaded into the Millenniums memory and that C-3PO is able to plug in and talk to it.