It will appear in the next update to the existing British Airways iOS and Android apps, and will presumably (on iOS) integrate into ‘Passbook’. The screenshots provided by BA look pretty smart:
… with most of the membership information currently found at ba.com copied over.
The introduction of the app-based card will coincide with the removal of plastic cards for Blue members. You will now have to achieve Bronze status or higher in order to receive a piece of plastic through your letterbox!