How do I create a view which is embedded in a Panel overriding the Drupal User Page, which shows the data from a CiviCRM profile ONLY to the currently logged in user, and that user has permission to see their own data in CiviCRM. The goal is to make a pane which shows some basic information about their civi contact record, so they can click a link, and edit it, and return to see it changed. Thanks!
To answer your question: "What permission would just allow users to see their own results of this view?"
Views Solution (if users still need to be able to visit other users' user-pages)
Picking up from Coleman's answer, using a contextual argument (we've used "CiviCRM Drupal match table: Drupal User ID" with success), you provide a "Default value" of 'User ID from the logged in user'. Then, to limit the view to be viewable by each user only, scroll down in the contextual argument window and "Specify Validation Criteria" with a "Validator" of 'User'. Only allow 'Numeric UIDs' and for "Action to take if the filter value doesn't validate", choose 'Hide View.'
When User X visits his/her own user-page, the view will display. However, when User X visits User Y's user-page, User X will not see the information the View provides.
Drupal Permissions Solution (if users do not need to visit other users' user-pages)
If authenticated users have the Drupal permission "View User Profiles" under the 'User' section, then all users who are logged in would be able to see the results of the view, if the view is otherwise unrestricted. If you remove that permission, your view would be limited to the logged-in user only.
You cannot embed a civicrm profile in a drupal view. Using the user id as an argument and a relationship to the contact, you should be able to construct a view that displays the contact data you want to show for the current user.
In the view header or footer you can place a link to either a civicrm profile form or a drupal webform with civicrm integration that will allow the logged-in user to edit their own contact record.