I have looked all around the mobile app - but I can't see where I see my goals and the status of how far along I am.
This is not a feature of the Explore app. The Explore app is aimed mostly at handling activities that create GPS tracks.
If this functionality is available at all via a mobile app, it would be in Garmin Connect Mobile. However, I don't see it there either. I don't use this feature much, so YMMV.