Siege mode was a feature of the Doctor's TARDIS that could be activated using a lever under the console to prevent entry or exit.
Additionally, it could protect the TARDIS when its shields were compromised. Siege mode required a sufficient amount of power to activate or deactivate. The Twelfth Doctor activated it when his ship was in the path of an oncoming train with no shields. While in siege mode, the Doctor's TARDIS no longer had the appearance of a police box, but of a small cube with Gallifreyan symbols along its sides.
When the Doctor initiated siege mode while the TARDIS had endured severe power drain by the Boneless, it exhausted its power supply and caused the TARDIS to shut down entirely. Its life support systems began failing, and the Doctor started running out of breathable oxygen. The TARDIS interior also became extremely cold, causing the Doctor to button his coat all the way up to the collar and turn the lapels up. After Clara Oswald and Rigsy tricked the Boneless into feeding energy back into the TARDIS, the Doctor was able to turn off siege mode and regain control over his ship. (TV: Flatline)
Behind the scenes
The webcast Stealing Series 9 Scripts mentioned "siege mode protocols" one of the many defence systems placed by Steven Moffat on his underground "secret writing lair" below 221B Baker Street. Said lair was also said to have a Hostile Action Displacement System, leaving no doubt as to whether the use of the phrase "siege mode" is indeed meant to reference the TARDIS feature.