Assume that you publish a Microsoft Access 2013 web app on a public Microsoft SharePoint 2013 site. When you try to access the app without being signed in to SharePoint, the app opens in read-only mode. Specifically, the menu bar buttons are disabled, and you cannot add, edit, or delete records.
This occurs because anonymous users (or individual users who are not specifically added to the SharePoint site) have read-only permissions to Access web apps on the site.
If you want to make edits through the Access 2013 web app, you have to first sign in to SharePoint as a user who has edit permissions on the SharePoint site. To sign in to SharePoint from the Access web app, click the Back to Site link in the upper-left of the window. You are then prompted to sign in. After you sign in to the site, you can return to the Access web app.