Matt Glaman: How do theme template overrides in Drupal work?

In Drupal, with themes, you can override default template output by copying, pasting, and customizing those templates. It works, but how? I thought I always knew how this worked. But I realized I didn't when I dove into supporting Drupal 7 themes with Retrofit.

I know Drupal builds the theme registry and theme hook suggestions. In doing so, it scans templates, and part of that process includes scanning the active theme for template and theme hook template implementations. But when reading the \Drupal\Core\Theme\Registry code, I was coming up blank.