The Actions button will display links to perform actions like adding a case note, uploading a document, etc. Like the layout of the profile page, the action links that are available are determined by site administrators.
Fields can be made editable on the profile page by administrators. A field with a clickable blue link, like Legal Problem Code in the example screenshot, can be edited.
A case's disposition affects which fields are editable as well as which action links are available. For example, after a case is closed, administrators may make most or all of the fields on the profile not editable, and may remove most of the action links, both to prevent information on closed cases from being changed without re-opening the case.