The feature is called screen pinning, and it’s been hiding in Android’s settings menu since Lollipop. (Look under “Fingerprints & security.”) Turn it on, and then you can “pin” a single app to the screen whenever you like.
While the screen is pinned, the kid can’t get out of the app with the usual back, home, or overview buttons. (That’s what the square button is called.) This feature is also handy if you want to keep a certain screen open but worry that you might bump a button by accident.