You can open a Mystery Box that you earned from a City by tapping on it on the Who Wants To Be a Millionaire home screen and then tapping on the “Unlock” button. You can only have one Mystery Box opening at a time. Mystery Boxes take some time to open, and each type of Mystery Box takes a different amount of time.
You can also purchase Mystery Boxes from the Mystery Box shop by tapping on the cube with a “?” on the home screen. Unlike Mystery Boxes that you earn from Cities, these Mystery Boxes open immediately, even if you already have another Mystery Box being opened.