Symbolism, Imagery, Allegory
The Ancient House is the only non-glass building in the entire city. It's a sort of museum, containing trinkets and artifacts from the world before the One State. It's also the only building in the city that permits any privacy. Small wonder that MEPHI uses secret tunnels hidden under it to move in and out of the city.
D-503 first sees the Ancient House as a representation of humanity's frustrating opaqueness, since "human beings are built as nonsensically as these stupid 'apartments,' human heads are opaque and there are only two very small windows that lead inside: the eyes." (6.34) True, but that opaqueness looks a whole lot better once D-503 starts to see where I-330 is coming from. He starts returning to it again and again, helping to accelerate his transformation.
In that sense, the Ancient House also represents the sleeping emotions of every citizen of the State. It's an anomaly amid overwhelming uniformity: a little seed of individual expression amid thousands of miles of solid glass. But like all those emotions, it holds the key to a larger, wilder world… one that might overwhelm all that stuffy glass and order. That secret passage underneath it leads to the outside world, which is very different from life in the One State. The House thus feels like a doorway, one that reveals all the things—all the wonders of life and ways of living—that citizens of the State could never feel. And just as D-503 becomes more and more human throughout the book, so does the House, its occupants (notably I-330) and its promise of escape becomes more and more important to his life.