Hi Anders,
Thanks for reaching out.
The Slack App ID is the Id of the App you installed in Slack workspace, it could be Sales Cloud for Slack, Service cloud for Slack or Salesforce for Slack (or even more apps). Once you installed any of these apps in the Slack workspace and then connected with your Salesforce credentials, after that which ever apps are installed in Slack and configured with Salesforce instances, those apps are visible under the Slack app: option which in turn evaluates to the Slack App Id.
Hope that helps.