Boat One was the presidential aeroplane of UNIT, created as part of an international agreement on incursion protocols. Under this agreement, in the event of a full-scale invasion a President of Earth with complete authority over every nation state was immediately inducted. It was decided the only practical candidate for this role was the Doctor. (TV: Death in Heaven) The Twelfth Doctor enjoyed using it for "poncing about". (TV: The Zygon Invasion / The Zygon Inversion)
This induction was performed during an invasion of Earth by an army of Cybermen converted from the dead by Missy. Having stumbled upon the invasion, the Twelfth Doctor was captured and taken aboard by UNIT, where he was inducted as Earth's president. Missy was also briefly contained aboard the aircraft.
During flight, the Cybermen attacked the plane. They broke the windows and dragged Colonel Ahmed from the aircraft, while also allowing Missy to escape her confinement. Missy tormented and killed Osgood, before breaching the hull and allowing Kate Stewart, the Doctor and the TARDIS to be blown out of the fuselage.
The Doctor flew in the plane to Turmezistan and back to the United Kingdom, returning with Osgood and a hostage Zygon. Bonnie, a Zygon disguised as Clara Oswald, fired at the plane with a missile launcher during its return trip. (TV: The Zygon Invasion)
Bonnie's first missile attack on Boat One missed, because the real Clara interfered with Bonnie's reflexes using the live link formed between them. Bonnie resisted further interference, kept the second missile on target and destroyed the plane. However, Clara had bought the Doctor and Osgood enough time to survive the attempt on their lives. They had witnessed the first missile brush by the aircraft and started to evacuate, and by the time the second made contact, they had already escaped and parachuted to safety. (TV: The Zygon Inversion)