The message, which shows up in the middle of your individual chats, reads: "Messages you send in this chat and calls are now secured with end-to-end encryption. Tap for more info."
And it essentially means that anyone from the outside looking in while find it nearly impossible to hack in and read your messages, unless they have your actual phone in their hands and then do an FBI by managing to work out your passcode.
Not even Whatsapp themselves can access your messages when they're encrypted like this. But it's not actually that big a change; the messages themselves have always been encrypted in the app. The only addition is that now every message, photo, video, file, and voice message sent is also end-to-end encrypted by default. This includes messages sent in group chats.[cosmo]