The narrator, a pilot, discusses his childhood attempts at drawing a boa constrictor eating an elephant. First, he draws the image from the outside, and all the grownups believe it's a hat—so the narrator attempts to draw the boa constrictor from the inside, and this time the grownups advise him to quit drawing boa constrictors and devote his time to other subjects like geography, arithmetic, grammar, or history instead.
The grownups have lost their imagination and ability to see the drawing for the truth it contains in the narrator's eyes—they can only jump to the most obvious conclusion that the hat-shaped creature is a hat.
The narrator chooses another profession instead, becoming a pilot. As a pilot, he claims that he has spent a great deal of time among grownups. When he meets one who seems clear-sighted, he says, he shows them his childhood drawing of the boa constrictor from the outside, but the grownups always say that the drawing is of a hat. As a result, the pilot brings himself down to their level, talking of sensible matters instead of stars, boa constrictors, or primeval forests.
If the grownups do not pass the pilot's boa constrictor test—and none of them do—the pilot dismisses their ability to see and appreciate the important things in life, like stars. Instead, grownups are more interested in the tangible, practical realities of everyday life, missing (or dismissing as pointless) the beauty and wonder.