Where do twig files find variables? for example for the file node.html.twig has a giant comment saying

* Available variables:
* - node: Full node entity.
 *   - id: The node ID.
 *   - bundle: The type of the node, for example, "page" or "article".
 *   - authorid: The user ID of the node author.
 *   - createdtime: Formatted creation date. Preprocess functions can
 *     reformat it by calling format_date() with the desired parameters on
 *     $variables['node']-&gt;getCreatedTime().
 * - label: The title of the node.
 * - content: All node items. Use {{ content }} to print them all,
 *   or print a subset such as {{ content.field_example }}. Use
 *   {{ content|without('field_example') }} to temporarily suppress the printing
 *   of a given child element.
 * - author_picture: The node author user entity, rendered using the "compact"
 *   view mode.
 * - metadata: Metadata for this node.
 * - date: Themed creation date field.
 * - author_name: Themed author name field.
 * - url: Direct URL of the current node.
 * - display_submitted: Whether submission information should be displayed.
 * - attributes: HTML attributes for the containing element.
 *   The attributes.class element may contain one or more of the following
 *   classes:
 *   - node: The current template type (also known as a "theming hook").
 *   - node--type-[type]: The current node type. For example, if the node is an
 *     "Article" it would result in "node--type-article". Note that the machine
 *     name will often be in a short form of the human readable label.
 *   - node--view-mode-[view_mode]: The View Mode of the node; for example, a
 *     teaser would result in: "node--view-mode-teaser", and
 *     full: "node--view-mode-full".
 *   The following are controlled through the node publishing options.
 *   - node--promoted: Appears on nodes promoted to the front page.
 *   - node--sticky: Appears on nodes ordered above other non-sticky nodes in
 *     teaser listings.
 *   - node--unpublished: Appears on unpublished nodes visible only to site
 *     admins.
 * - title_attributes: Same as attributes, except applied to the main title
 *   tag that appears in the template.
 * - content_attributes: Same as attributes, except applied to the main
 *   content tag that appears in the template.
 * - author_attributes: Same as attributes, except applied to the author of
 *   the node tag that appears in the template.
 * - title_prefix: Additional output populated by modules, intended to be
 *   displayed in front of the main title tag that appears in the template.
 * - title_suffix: Additional output populated by modules, intended to be
 *   displayed after the main title tag that appears in the template.
 * - view_mode: View mode; for example, "teaser" or "full".
 * - teaser: Flag for the teaser state. Will be true if view_mode is 'teaser'.
 * - page: Flag for the full page state. Will be true if view_mode is 'full'.
 * - readmore: Flag for more state. Will be true if the teaser content of the
 *   node cannot hold the main body content.
 * - logged_in: Flag for authenticated user status. Will be true when the
 *   current user is a logged-in member.
 * - is_admin: Flag for admin user status. Will be true when the current user
 *   is an administrator.


Where would these come from?  

When I write my own template file how do I know what variables are available in my new template file?
Variables can be added and manipulated in preprocess functions just as with .tpl.php files. 

Twig has a dump() command that can allow you to see the available variables.