Whispering is what you do when you speak so softly that you can barely be heard. Most teachers have a rule that there's no whispering allowed while the class is taking a test.
Whispering involves using your breath, rather than your vocal cords, to speak very quietly. You might hear whispering in the quiet section of the library or during a play or movie — it's used for communicating secrets or simply to avoid bothering other people. The word can also be used as an adjective for sounds that resemble a whisper, like the whispering wind through the trees on a breezy day.