what's are these "@name" and "@site-name" token-things in email_example.module and how do they work? In the dgo.to/example module's email_example.module's hook_mail() function there's this line:

      $message['body'][] = t('@name sent you the following message:', array('@name' =&gt; $user-&gt;name), $options);


I haven't seen @thing used that way before?  How does that work?  What convention is that?
Please refer to the official D8 Sanitizing Output Documentation.

From the documentation page

There are three available placeholders in Drupal 8:


@variable: When the placeholder replacement value is a string or a MarkupInterface object
%variable: When the placeholder replacement value is to be wrapped in em tags.
:variable: When the placeholder replacement value is a URL to be used in the "href" attribute


You can learn more about these placeholders in the FormattableMarkup::placeholderFormat() documentation.

EDIT FOR DRUPAL 7:

See this documentation https://www.drupal.org/docs/7/api/localization-api/dynamic-strings-with-placeholders

The variables/tokens available for use as replacements is dependent on the context of the surrounding code and whether or not the script is called via Apache or from the command line.