Whisper is really just a way of speaking, not a phonation mode that provides for contrastive sounds. Nevertheless it is a distinctive and common way of using the vocal folds that speakers of all languages employ, so it usually gets treated in linguistics courses as one of the five ‘modes’.
Whisper involves holding the length of the ligamental folds closed, while holding the arytenoids wide open.
Play the movie to see that the ligamental folds close right up, and the arytenoids are held wide apart to form a small V-shaped opening. Note that the false vocal folds and parts of the larynx above the folds are all constricted tightly as well. You will see that there is no actual phonation – the vocal folds don’t move.
In Whisper mode airflow is forced through a much smaller opening than in Voiceless mode. The turbulence generated at this narrow opening acts as the actual sound source. Of course voiceless turbulence is a very poor sound source compared to real vocal fold phonation, which is precisely why this mode is great when you don’t want your voice to carry!
Note that, without phonation, much of the contrast between voiced and voiceless sounds is lost in this mode. However, try whispering ‘pea’ and ‘bee’, and you’ll probably find that other cues, such as aspiration, still enable you to distinguish between them.