A title is a story's first impression. People make a first impression with appearance, wardrobe and body language. Stories do it with a title. So I think titles are extremely important. A title creates anticipation and expectation or, perhaps, disinterest. Often the title is what will determine whether or not someone reads a story. Which of these three stories are you most eager to read?
The World's Room
They Who Get Shot
A Farewell to Arms
Ernest Hemingway considered the first two titles before he settled on the final one. He made the right call, don't you think? Hemingway asserted that a title must have magic, and I'd say A Farewell to Arms does indeed have a little magic.
This, of course, leads to the question of where to find a good title. Look for something that interacts with the story in an interesting way. Mary Gaitskill's short-story collection Bad Behavior might make a reader think the stories explore that-‑bad behavior--and they do, but they also delve into different value judgments of “bad." The title of Russell Banks's novel The Sweet Hereafter might make some think of aftermath; others, heaven. The novel explores both through a town's reaction to the loss of their children in a bus crash, but it is not “sweet" in quite the way we might anticipate.
Many titles spring from these sources:
Character: Vladimir Nabakov's Lolita, Ron Carlson's “The Ordinary Son"
Place: Willa Cather's The Professor's House, Robert Morgan's Gap Creek
Event: Eudora Welty's “Why I Live at the P.O.," Jhumpa Lahiri's “When Mr. Pirzada
Came to Dine"
Object: Kurt Vonnegut's “Bagombo Snuff Box," Barbara Kingsolver's The
And there's nothing stopping you from finding something unexpected or inherently unique to your story. Lorrie Moore uses an observation for “People Like That Are the Only People Here." Ray Bradbury used a temperature for his novel Fahrenheit 451. It would be impossible for you to glean what those stories are about through the title alone, but those titles certainly make you interested to find out, don't they?
That's the secret of a good title. It makes you want to start the story.