How to move block functions into .inc file?
The files directive is used to include files containing classes, check documentation.
You could include the file in the .module file.

require_once __DIR__ . '/includes/blocks.inc';


Edit: Included the other solutions added by @Beebee and @Jimajamma in the answer:

require_once  drupal_get_path('module', 'mymodulename') . '/includes/blocks.inc';
module_load_include('inc', 'MY_MODULE', 'FILE_NAME');
// This method is including a file residing in the module folder not in a subdirectory.