What exactly is the global context?
It means the global scope, ie anything outside a function and namespace. It's the PHP 'global', not anything specific to drupal.

People tend to use module_load_include at the top of .module files to bring in includes, much like in a traditional standalone PHP project.

This is potentially bad because the required elements might not have been bootstrapped at that point, which can lead to errors; hence the warning not to use it in a global context.