Craft time! Kids can make their very own Whisper-ma-Phone—if you've got an old "snergelly hose" lying around somewhere, that is. Hopefully though, they don't have any secrets that people would pay to hear.
This image of covert communications appears only once, right at the beginning of the story. The Whisper-ma-Phone is the device through which the Once-ler's entire confession is delivered. In fact, the boy, his ear to the ma-Phone, is the last thing we see before we're plunged into the Once-ler's flashback.
What's the purpose of this strange device? Well, it definitely foreshadows the communication issues highlighted by the Once-ler's story, and at the same time, proposes a novel solution: listening—even when something might be hard to hear. After all, it's hard to understand the Once-ler because the snergelly hose makes him sound "as if he had smallish bees up his nose" (50).
In spite of this bad connection, the boy seems to be listening very attentively. By contrast, neither the Once-ler nor the Lorax is able to listen to the other. If they'd gone to the trouble of listening, they could have shared their secrets and reached a compromise. (There's definitely a lesson to be learned in there.)
All this secrecy also just boosts the suspense for super-young readers—just like older readers, they'll love the idea they are hearing something not meant for just anybody's ears.