Hierarchy System
When Wordpress needs to load something, it doesn't automatically go to one specific file. Instead, it checks for a lot of other files until it finally reaches one that exists. This isn't anything you need to configure either; Wordpress will search for those files based on name, so as long as you create one, you're set. Making template files becomes an easier way to manage and customize your Wordpress site. Thinking about it, it might not be possible to do much at all with your site without template files since every post and every page are initially run by two files, but I could be wrong.
Order
Ordering goes from most specific to least specific. If nothing else exists, everything will always end up at index.php since you can't make a site without that file. Otherwise, there appear to be seven different paths, six pages and one embed, with the deepest path being 10 files long. Most of the named pages follow one path, but I do see two instances where they branch off into two paths: front-page and $custom.
File Naming
As mentioned, file naming is the way to make this work, so you can't just name everything what you want. The higher you are in the hierarchy, the more specific/informative you need to be. One convention used a lot is looking for a slug, then looking for an id. Since slugs are the custom and more detailed option, it will look for these first. Slugs are the names associated with something, while IDs are just the non-specific representation of records in the database. I know that IDs are specific in the sense of uniqueness, but you don't have control over them.
Summary
You don't necessarily need to memorize the hierarchy if you want to make a good site, but you should remember to reference it. Without it, your site might end up more disjointed or not working at all.