Whispering is a way to talk "quietly" to someone near you, so that people who are not near you will not hear what you say.
This is not used frequently, since if you want to send anything to only one person you can use private messages.
When you whisper, only players adjacent to you (1 sqm) will hear you. Any other players on the screen will only hear "pspsps".
To whisper, on the default channel, lower left corner, there is a small microphone icon; click one time to yell and twice to whisper. You can also whisper by typing "#w" before your message.
Prior to the implementation of sound the whisper icon appeared as 
whereas it's current appearance is 
.