I've seen that when I create an Autohosted App for SharePoint 2013 (or any other type of Apps), I'm then able to add a new item to the SharePoint Project such as a List.
I can then add/edit/delete fields of this lists through Visual Studio but when I deploy the App on my SharePoint-Online site, I can't see if or where the lists are created.
Are the lists in my App available somewhere on my site when my app is published?
"The APPWEB URL"/Lists/"The list internal name"
But really you should access the list (CRUD items) via Client object model or REST.
Benefit: This approach enables you to reuse common SharePoint artifacts, such as lists and Web Parts.
So, you could use a List also in the other hosting alternatives, it will be added to the App Web though.
We can create our custom SharePoint artefacts like list,content types as part of our Auto Hosted or Provider hosted apps too and not only in SharePoint Hosted apps.
Your feature and list will be deployed in the AppWeb which is a subsite that gets created whenever a new app is created. So instead of checking for the list and the feature in the host web, You can see them as part of the AppWeb.
You can find the AppWeb's url from Site Settings->Site Collection Administration section->Site hierarchy, Title will be your App name.
Once you know the url, You can visit the manage features page of the App Web through "URL_of_app_web/_layouts/15/ManageFeatures.aspx". Here you can see your feature already activated if it has been properly deployed.
And to see your list visit "URL_of_app_web/lists/list_internal_name". Here you can see your list along with his items.
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