WordPress does not have such an option by default; you will have to create the functionality for per-post background images – which is entirely possible.
Your best bet might be to use post custom meta to link/upload per-post background images, and then enqueue a dynamic stylesheet that applies that image as the background for the post, using the .postid-$id CSS class.
- Create a custom post meta box
- Add to the meta box a form field to allow the user to provide a URL to an image, or to upload an image
- Enqueue a function that queries the
post_custom_meta(), and applies the background style if the appropriate post custom meta data exist.
EDIT
If you just want to know where that background image CSS definition is being applied: it is being enqueued, as a callback function likely to the wp_head or wp_print_styles action hook. You’ll need to look in functions.php for this callback function.