What does the two speech bubbles notification icon means? What does the two speech bubbles icon (second from the left) in the notification bar mean?
It is a notification from one of the chat apps you may have installed (e.g. Facebook).
It is either notifying you of new messages (which will be cleared when you pull down the notification tray and click on it) or it is trying to make itself persistent so that the system will not remove it from RAM memory (which you can unset it in the settings of the app) which will affect user experience.