Your Apple App Store ID is required when creating a new app in Button. This is so that when a user clicks your Button in a publisher's app and the user does not have your app installed on their device, the publisher's app can correctly bring up your app in the App Store for the user to download.
https://itunes.apple.com/us/app/button-partner-app/id1112017950?mt=8
and your App Store ID will be 1112017950
When you create an app, it will ask you for your "Store ID"
If you have already created an app and did not add your app store ID at the time of creation, you can add it from the Dashboard after clicking into your app.