The "illogical house" was a psychic projection of, and metaphor for, the Doctor's long and contradictory life - the sum of all their memories, including the erased ones from their secret past. It was contained within the biodata module used by the Division to erase the Doctor's memories following their service as their agent, (TV: The Vanquishers) which was kept by Tecteun at Division Control in the form of a fob watch. (TV: Survivors of the Flux)
After Chris Cwej had shared an adventure with the Seventh Doctor in his crumbling ancestral hall, the House of Lungbarrow, and witnessed the similar new interior adopted by his other home the TARDIS, Cwej reflected that "shadowy corridors, alcoves and stairways, a secret at every turn" were "like being in the Doctor's head" and also "like his life, for that matter, the details of which were strewn like flotsam across the floor". (PROSE: Lungbarrow)
After having had a premonition of the illogical house while she was unconscious from having been thrown through time by the combination of the Flux and Vortex energy from the heart of the TARDIS, (TV: War of the Sontarans) the Thirteenth Doctor found herself faced with the illogical house after the Ravagers Swarm and Azure opened the fob watch containing her lost memories about her past as the Timeless Child and an agent of the Division.
Azure described it as "a construction that makes no sense", with Swarm explaining that "all the memories [she'd] lost, all the people [she'd] been [were] all in there, contained within that house". He taunted the Doctor with the knowledge that if he let her go inside, she could literally "meet the selves [she'd] lost". Instead, however, Swarm and Azure used their powers to disintegrate and reshape the house at their whim, a process which also unravelled the Doctor's consciousness. Although they stated they could have rendered it all to dust, their only did this slowly and haltingly before eventually pulling the Doctor back out of the mindscape within the watch. This was because they intended not to kill her then, but instead to bring her as a sacrifice to Time themself.
After the Doctor managed to extinguish the Flux, leading Time to destroy Swarm and Azure for their failure, she retook possession of the fob watch and chose to drop it down a chute in her TARDIS to remove the temptation of ever opening it again. (TV: The Vanquishers)
Other references
When the Fifth Doctor visited the Eye of Orion along with Tegan Jovanka and Vislor Turlough, he suddenly started to feel what he described as cosmic angst, which was a result of President Borusa using a Time Scoop to bring the Doctor's past incarnation to the Death Zone on Gallifrey. The Doctor described the act as him "being diminished. Whittled away, piece by piece" and told his companions that "a man is the sum of his memories, y’know. A Time Lord even more so.". (TV: The Five Doctors)
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