Kindness, sincerity, and openness seem like significant character traits of the narrator's wife. Since she sleeps through much of the present action of the story, the background information the narrator provides is vital to understanding her. If we didn't have it she'd be a bare sketch. This background information influences how we view her actions in the story.
Her journey in the story seems similar to the narrator's. She has assumptions about her husband, similar to those he has about Robert. She doesn't understand that he's jealous, and she assumes he's going to be mean to Robert. We can also see that in trying so hard to make Robert feel comfortable, she's forgetting about her husband's comfort. She doesn't seem to understand that meeting Robert might be awkward and even painful for him.
We know more about her past than we do the narrator's. But, we know more about his present than we do hers. Getting at her present state requires a little imagination. Throwing a potato on the floor when she's frustrated with her husband (1.13) seems like a big clue. We think it suggests there's some anger there that extends past this single night. Since she's taking her anger at the narrator out on an innocent potato, the moment also suggests that, like him, she's having trouble positively communicating her feelings and needs.
But wait, didn't we say she's straightforward? Yes, we did. She seems to be candid with Robert. And, by the narrator's own admission, she tells him everything. She tells him straight-up about Robert, right down to the face-touching. Not like she's confessing, but more like she wants him to appreciate the wonder of the experience (which he probably does by the end of the evening). She's perfectly blunt with him about what she wants out of him in terms of Robert. She even presents it as an ultimatum: "If you love me […] you can do this for me" (1.8). But, she probably wouldn't be talking to him like this if their marriage was on solid ground. Just because she's straightforward doesn't mean she's communicating positively.
According to the narrator, the woman was already deeply dissatisfied in her first marriage after the first year. He says she told Robert, via tape that "she loved her husband but didn't like it where they lived and she didn't like it that he was part of the military-industrial thing" (1.4).
"Military-industrial thing" refers to a phrase coined by the 34th President of the US, Dwight Eisenhower. It refers to the relationship between a military force and the industries that produce the weaponry and other materials the military force needs. The woman didn't want to be directly involved in the complex at all. As the wife of a Navy officer, she was involved. Another problem was that she and her first husband were constantly moving from one military base to another. According to the narrator, she said this was a big factor in her suicide attempt:
This went on for years […]. […] one night she got to feeling lonely and cut off from all the people she kept losing in that moving-around life. She got to feeling she couldn't go it another step. She […] swallowed all the pills and capsules in the medicine chest and washed it down with a bottle of gin. (1.4)
This passage gives us lots of information about who she is, and what she wants and needs in life. It suggests that she makes friends easily, but "keeps losing them in the moving-around life." This helps us understand why her relationship with Robert is so important. She can't "lose" him, no matter how many times she moves. The passage also suggests that she desires a stable life, in one place, where she can form lasting friendships.
The narrator seems to have provided his wife with a more stable life. We know that he's been in the same job for three years, so presumably they haven't been moving around a lot. But something is still missing. The woman and the narrator aren't connecting and she's still (presumably) lonely. And that might have something to do what she says to the narrator in the kitchen:
You don't have any friends, […] period. (1.10)
This doesn't tell us that whether she has friends, but it does tell us that she and the narrator don't have mutual friends. If she can't share friends with her husband, she's probably still feeling isolated. He's giving her stability, but also, perhaps, isolating her. Perhaps he's even driven away her friends with his surly attitude. This would help explain her fears that he'll make Robert uncomfortable.
Right now, the woman needs her husband to not drive Robert away. Robert is her oldest friend, and the relationship is important to her. At this point, she probably doesn't dare hope for as much as Robert and her husband being friends. That she wants them to be is evident in all her previous attempts at getting her husband to understand their relationship.
In the narrator's "Character Analysis" we talk about the process of change he undergoes in the story, and the possible consequences of these changes on his life. We suggest in a few places that the narrator and his wife take similar journeys, though hers seems less dramatic and obvious than his. Like the narrator, she has quite a few drinks, eats a big meal, and smokes marijuana. But instead of something happening to her, she falls asleep. She wakes up again, too. Like the narrator, she has what Carver would call a "sudden awakening," though hers is a literal awakening from a literal sleep:
My wife opened up her eyes and gazed at us. She sat up on the sofa, her robe hanging open. She said, "What are you doing? Tell me, I want to know." (3.36)
The evening has gone well enough, and that's all she wanted. The two most important people in her life (that we know of) are with her and they are doing OK. This contented sleepy scene is a vivid contrast to what she wakes up to.
She opens her eyes to a scene of awakening, of creativity, and of intimate human connection. She can't process it with her eyes. Even after Robert tells her they are "drawing a cathedral" (3.38), she can't understand. She asks again, "What's going on? Robert, what are you doing? What's going on?" (3.39). These are her last lines in the story. Subtly, she seems to embody Carver's quote about "sudden awakenings." Here's the full quote again:
I have a three-by-five[card] […] with this fragment of a sentence from a story by Chekhov: "... and suddenly everything became clear to him." I find these words filled with wonder and possibility. […] There is a bit of mystery, too. What has been unclear before? Why is it just now becoming clear? What's happened? Most of all - what now? There are consequences as a result of such sudden awakenings. (source)
What has been unclear before for the woman? The narrator's love for her has been unclear. That the narrator and Robert are capable of connecting was unclear. Carver's questions "What is now becoming clear?" and "What's happened?" are spoken through her. It doesn't seem by chance that Robert speaks the following words right after she wakes up: "Put some people in there now. What's a cathedral without people?" (3.38).
We've talked a lot about the importance of people in her life, and that she seems to wish her husband was more of people person. Robert knows all about this, because she's told him. His instructions to the narrator might be his way of telling her that her life with the narrator will include more people now.
When she realizes that her husband is capable of much more than she thought, she might need to re-evaluate their relationship. Of course, the fact that he has this experience with Robert doesn't necessarily mean he'll change, or that all their problems will be solved. But, it might mean that there's more hope than she thought. Her mystified reaction to what she sees when she wakes is also a nod toward the story's message that eyesight is overrated. She can see what's going on, and Robert even tells her. The flood of complicate emotions the scene produces what is probably a healthy confusion, an awakening of perception. To understand it she'll need to use more than just her eyes.