This will open a list of all your notifications on a new page. This button is located in the upper-right corner of your notifications list. You’ll see any private messages sent to you by your friends here. This will open your chat thread in full-screen. You can read all the messages in the chat, and send a reply to your friend here.

Summary:
Tap the square speech bubble icon at the bottom of your screen. Tap the inbox icon on the top-right. Tap a message in your inbox.