The green "Mention" box refers to the feature that allows you to direct a public message to a particular user in the chat room. When you click a user's name and choose "Mention" your message will be visible to everyone in the room, and the user you directed the message to will hear a tone or sound, indicating that they have been mentioned. This helps to get the attention of a specific user in a public chat setting.
Please use this sparingly, a better option for ongoing discussions is "whisper". Whisper messages are not seen by everyone.