The literary insight essay invites you to express your own feelings and ideas about a literary work (a short story, a novel, or a play). In this type of essay you are usually not asked to do research (especially not just to copy statements from professional critics about the story you are analysing). Nor is this a book report, so you do not want to summarise the plot; assume that the reader has already read the story. Instead, the reader is interested in your interpretation of the story. What makes such an essay valuable is your perceptions (as different from anybody else’s) about this particular piece of literature.
You may be interested to write about some feature of the story: its symbolism, imagery (a visual metaphor important to the theme of the story, ex. The image of dying flowers in D.H. Lawrence’s "The Odour of Chrysanthemums"), irony, setting, point-of-view, motifs (recurrent elements, ex. Darkness recurs in "The Odour of Chrysanthemums" to create suspense and to signify death and alienation), important contrasts or similarities in the story, or characterisation. Whatever you write about, your purpose is not to make your readers like or dislike the story, but to help them see things that they may not have seen before.
Start by freewriting about the question you have been asked or the topic you are considering: write your first impressions quickly to get your ideas on paper. Among other things, you should focus on the details – the symbols, the connotations of key words, the characters’ gestures, and perhaps a few key sentences that puzzle or surprise you. This will necessitate reading and re-reading the story. Close reading leads to close analysis. Make extensive notes, digging deeply into the story. After a while, you will find some central interest or idea emerging out of your notes. This idea will become the crux of your paper, your thesis, the central idea that you want to convey to the reader.