You can't directly use maps from ArcMap on the web. You need to publish your map as a web service. There are two ways to do this:
1. Publish to your own ArcGIS Server.
2. Publish to ArcGIS Online and create a hosted service. You need a subscription to ArcGIS Online to do this.
ArcGIS Online lets you create web maps that reference services. These web maps can be consumed in many different client applications, like Android apps. I can't tell you exactly how to write your code. Looks like you already found the Android forum, that is the best place for coding questions.
It is possible to create web maps where a small amount of data (less than 1000 features) is directly loaded into the web map via a shapefile or CSV file. These would also display on an android client app.
Accessing web maps requires the app to be connected to the internet.
Thanks,
Mike