Giovanni's room is a place. It's a sanctuary. It's the one spot where David and Giovanni feel free to act out their desires hidden from the judging eyes of the world. Yet, the longer that David is there, the more it begins to feel like a prison. As the story goes on, we find out that the room has, in a way, been serving as a prison cell for Giovanni for a long time.
It is not surprising that the room takes on significance for the reader since it holds such significance for the two main characters. Giovanni and David begin to associate all sorts of emotions and ideas with the room and the result is that it ceases to just be a literal room. Giovanni's room is raised to a figurative level. It becomes a metaphor for the dream of David and Giovanni's life together and, later, for the impossibility of realizing the dream.
Several times in the novel, Giovanni resolves to renovate the room. David observes that the room is an utter mess, that its garbage is the refuse of Giovanni's wasted life. Toward the close of the novel, when things are not going well between them, Giovanni tries to carve a bookcase into the wall. He pulls away plaster and brick, and David senses that it's like he is trying to enlarge the room whose walls seem to be closing in on him.
The room, then, is what we might call an embodied metaphor. It takes on metaphorical connotations, but it is a real room and almost all of its metaphorical value is linked to experiences that actually take place in that room.
But here's an interesting and slightly complicated twist: the figurative does not simply steal its significance from the literal. As the tragedy progresses, one begins to learn that the process works both ways. For example, the idea of the room as Giovanni's prison cell ceases to be just an idea and Giovanni's cell becomes a literal reality.
In short, the title focuses us in on a nuanced and complicated metaphor that lies at the heart of the book. It forces us to ask the questions: what is the relationship between the literal and the figurative? What is the relationship between the real and the imagined?