I tend to think that this is one of the best lines in the novel. I think that it really captures the pain of the foreign exchange student quite well. Being one myself in Europe, I tended to immediately identify with Changez at this moment.
The setting of the quote is that Changez, in his kurta dressed best, has gone to visit Erica's home and her parents. When he arrives, she takes him to her room. It is a room that is clearly lived in. Changez absorbs what it is to have one's own room, one's own space. There is clear definition as to this room, this space, being Erica's. It was "home" for Erica, and something that triggered a sense of longing in Changez. When he says that he "longed for the settled nature of my past," it reflects how much he does miss a space he can call home. Changez has lived in dormitories, shared space with other people, lived in settings where boundaries for personal identity have been clearly established with lines demarcated for use. He has lived in collective settings that were living arrangements. He has missed the concept of "home" and he feels that with Erica. It is a moment where one sees the questioning of this pursuit of "the American Dream" for Changez. It is an instant where the unbridled pursuit of freedom in America could be easily exchanged for some type of grounding or feeling that one belongs. Naturally, this applies to Changez's life as a student. Yet, it could very well be a statement on how he feels in America after September 11. America, complete with its hostility towards individuals of the Muslim faith, could not have seen like a "home" but more like a "house." It might not have seen as an arena for settling down and establishing roots, but rather a workplace, or a temporal setting where individuals are. It is in this idea of a "settled nature of the past," one can see that beneath Changez's belief of living a charmed, movie star life, there exists a certain amount of displacement at being a hyphenated American, a stranger in another's country.