Thanks, @LeBraat!
The app card is for adding to web pages so that when a link to that page is posted in a Tweet, an app card will be shown directing users to their appropriate app stores.
If you are an advertiser, you also have the option to generate app cards via the ads dashboard. You can read about that here on our Twitter for Business portal.
There was a short-lived experimental beta feature where some mobile apps were featured directly on company profiles, but that feature is no longer available.