Whisper mode will likely be most useful around children, whether it's to get the kids in the mindset that it's bedtime and they should be quiet, or to avoid waking a sleeping child. Users can whisper normal Alexa commands and the smart assistant will whisper right back to you.
The idea behind this feature is training Alexa to recognize conversational cues. For example, if you were having a conversation with someone and lowered your voice to a whisper, the person would naturally respond in-kind. This kind of feature will make Alexa seem more natural in Amazon's view.