Cathedrals don't make an appearance in this story until the third section, and then it's fairly obvious why the story is called "Cathedral." Cathedrals are the subject of the television documentary and of the narrator and Robert's drawing. A cathedral is a cathedral is a kind of church. There aren't any secular (nonreligious) cathedrals. Most critics don't see "Cathedral" as having explicitly religious themes, though such themes aren't excluded. A much smaller group of critics see Carver's work, including "Cathedral," as espousing Christian principles. Since the evidence we see leans toward the secular view, that's the view we're exploring in our discussion of the title. If you disagree with us, we hope our discussion provokes an interesting essay.
None of the characters seem to be actively religious, but the woman's religious views aren't discussed. Similarly, we don't know if Robert is a religious guy, but we do know that he's never given cathedrals much thought until this evening. The narrator's point of view is presented most clearly in this conversation:
[Narrator:] "In the olden days, when they built cathedrals, men wanted to be close to God. In those olden days, God was a part of everyone's life. (3.14)
[Robert:] "Let me ask you a simple question, yes or no. I'm just curious and there's no offense. You're my host. But ask if you are in any way religious? You don't mind my asking? (3.15)
[Narrator:] "I guess I don't believe in it. In anything. Sometimes it's hard." (3.16)
There's nothing to indicate he changes his mind about religion by the end of the story, but maybe he does learn to believe in something, like maybe that he needs a friend and has found one in Robert.
The narrator's position is basically an echo of Carver's own views on the subject of religion. When asked in an interview whether he was religious Carver answered, "No, but I have to believe in miracles and the possibility of resurrection" (source).
Cathedral are massive structures "that took hundreds of workers fifty or a hundred years to build" (3.9). They require lots of special materials, design, and tools. Conversely, the drawing of the cathedral is built by a couple of men, in less than an hour (roughly), using basic materials. So maybe getting closer to each other is less complicated and difficult than getting closer to God. Of course, the drawing of the cathedral only influences the three people in the room. It's isn't likely to physically withstand the test of time. A cathedral remains for thousands of people. Still, the drawing isn't necessarily the important part of Robert and the narrator's experience. What's important is the experience itself, and how it impacts their lives after the experience is over.