Add custom objects/entities to WordPress

I think what you want is to create what WorpPress calls “Custom Post Types”.
Please have a look at the Post Type page in the Codex that explains what Post Types are and how to create custom ones.

Basically, here is the code to create the Object custom post type :

add_action( 'init', 'create_post_type' );
function create_post_type() {
  register_post_type( 'object',
    array(
      'labels' => array(
        'name' => __( 'Objects' ),
        'singular_name' => __( 'Object' )
      ),
    'public' => true,
    'has_archive' => true,
    )
  );
}

A side note : in your screenshot, the WordPress version seams very old (3.3 or something). Please Upgrade to the latest version to take advantage of the new features.