James Thurber's essays are all autobiographical, meaning he speaks about his own life. He uses subtle ironic humor to laugh at himself and his family of relatives as a representation of what he sees as the problems of then modern society.
What this means is that Thurber pokes fun at himself by pointing out how what he does and believes (and his family also) doesn't really fit with what life calls for. While he does this, he is also giving his opinions on the largersocial problems that either relate to or are the cause of the things about himelf and his family that he pokes fun of.
Irony is defined as the thing that happens instead of the expected thing, like a parent asking a child if s/he wants a milkshake, getting a "yes" answer, buying it and then proceeding to walk away drinking it. This is ironic: this is something happening that was not expected. [And of course the parent will realize the error and turn back and give the child the milkshake or buy a second one...]
In the essay "My Secret World of Idiom," Thurber tells how as a boy he learned to find the literal imagery within figurative idioms, building himself special fantasy lands that he kept to himself, a secret from parents and everyone. An idiom is a figure of speech that makes a point through language that means something different than what it says.
For instance, if I say "I'll plunge in to the deep water!" you might think I'm talking going swimming and diving in at the deep end of the pool. If you were Thurber, you'd build a fantasy image of just that, creating a setting for a swimming pool and an image of me diving into the deep water of a beautiful swimming pool. However, "I'll plunge in to the deep water!" is an idiom (actually two idioms put together) that really means "I'll get started on this hard project right away." An idiom uses figurative language that lends itself to imagery to say something else.
In his essay, Thurber tells the tale of his secret adventure with idioms to explore the creative mind, the power of imagery, the allure of figurative speech and the role of idioms in society. He also explores the loss of imagination and of the ideal by telling how one day his female cousin Frances explained all about idioms and collapsed Thurber's secret world built of the uncanny imagery of idioms around Thurber's head, meaning she broke the spell of the power of the imagery within idioms.