A number of John Cheever's stories contain everyday, normal people, many of whom are losers, those who never achieved the "American Dream" and ended up settling for familiarity and complacency. This is definitely true of "The Wrysons." Irene and Donald are what might be called NIMBYs, which means Not In My Back Yard. They are suburbanites who want their lives to remain familiar and comfortable. If the world changes around them, so be it; just as long as the changing world does not affect them. In other words, they don't want any change to occur in their back yards (their suburban town).
Irene's dream represents her fear of change. It is hyperbolic which is to say that Irene fears change so much that for her, change would be like the end of the world.
She cried, and she went on watching, as if some truth was being revealed to her—as if she had always known this to be the human condition, as if she had always known the world to be dangerous and the comforts of her life in Shady Hill to be the merest palliative.
Irene's comfort zone, the unchanging Shady Hill, was like living in a bubble. Anything that would disturb that bubble would be as if a hydrogen bomb went off.
Despite their security blanket of Shady Hill, Donald needs to be comforted now and again. The best 'palliative' for Donald is baking because this makes him recall the most secure times he had with his mother. Donald clings to security and stability as much as, if not more than, his wife.
In the end, Irene and Donald discover something they never knew about each other. This presents them with a chance to grow, at the very least in their relationship. What else might they not know about each other? What else could they discover? We are left with the impression that Irene and Donald treat this night in the kitchen, not as a bonding/growing moment, but as an aberration to be ignored. They reject this opportunity for change just as they have done for years. The hydrogen bomb dreams and the baking represent things that make this extremely dull couple at least a bit more interesting. But they do nothing with this new knowledge. They retreat to their familiar lives. Although they are "more mystified by life" they are still more interested in keeping up appearances (making things look okay even if they are not.)