THe three parts are Mosque, Caves, and Temple.
You might have noticed that the novel is not only divided up into chapters, but it is also divided into three parts entitled "Mosque," "Cave," and "Temple." The parts are also organized by the three seasons in India: "Mosque" takes place during the cool weather, "Cave" during the hot weather, and "Temple" during the rainy season.
These part divisions set the tone for the events described in each part. In "Mosque," the first part of the novel, Aziz's reference to the architecture of the mosque as that of "call and response" harmonizes with the general tenor of this part of the novel, where people are meeting each other at various social functions. Like the cool weather, people are generally calm and friendly.
In contrast, the "Cave" section of the novel contains the climax of the novel. Taking place during the hot weather, emotions are inflamed, and nobody seems to be able to think coolly and rationally. Just as Mrs. Moore's hold on life was threatened by her experience of meaninglessness within the cave, the entire community of Chandrapore is turned upside down as riots and unrest surround the trial.
Finally, the "Temple" section attempts to wash away the chaos of the "Cave" section with its pouring rains. In keeping with the Hindu motif of the temple, the chapter celebrates the Hindu principle of the oneness of all things with Godbole at the Gokul Ashtami festival, and provides us with a reconciliation, though a tenuous one, between Fielding and Aziz.