If someone is "following" you, you have the option to "shout" at them using a button on their profile page. They can shout back if you are following them. Shouts received by a person are semi-private, being visible to all those the person is following. When you receive a shout, an "alert" shows up in the header bar, and you have the option of receiving an e-mail notification.
Just open your mouth wide enough.... Then yell loudly until some one hears you.
You send a shout to the ones who follow you and who you follow and you shout at them. Not literally shouting, but this is what it is called. I would rather have it called a chat box since no one shouts to each other literally unless they are excited or mad.