The spacecraft that carries Princess Leia at the beginning of Star Wars is Tantive IV. It is a CR90 corvette serving as the diplomatic vessel of Alderaan, and Leia is aboard it while secretly transporting the stolen Death Star plans.
The original 1977 film opens with Tantive IV being pursued and captured by the much larger Imperial Star Destroyer Devastator. Darth Vader boards the corvette, searching for Leia and the plans. Before her capture, Leia gives the stolen data to the droid R2-D2, who escapes with C-3PO in an escape pod.
Tantive IV is often confused with the Millennium Falcon because both are associated with Leia and the Rebel cause. The Falcon, however, belongs to Han Solo and becomes important later in the film. An X-wing is a Rebel starfighter, while a Star Destroyer is the Imperial capital ship that overtakes Tantive IV.
The ship’s name was initially difficult to hear in the film and was not always emphasized in early dialogue, but later Star Wars reference material established Tantive IV as its official designation.