The codex puts it nicely:
One way to change the default behaviors of WordPress is using a file
named functions.php. It goes in your Theme's folder.
The functions file behaves like a WordPress Plugin, adding features
and functionality to a WordPress site. You can use it to call
functions, both PHP and built-in WordPress, and to define your own
functions. You can produce the same results by adding code to a
WordPress Plugin or through the WordPress Theme functions file.
The code in question is a function that is being called at runtime, which is pulling a file called /css/awsomew.css into the themes frontend. This file is located at ...wp-content/your-theme-name/css/awsomew.css. For more information on the wp_enqueue_style() function, see the codex as well.