I realise all content actually lives on the parent server and is held in domain folders.
It sounds to me as though you're not clear on the concept of CDNs. A true CDN is a global network of servers which is optimised for performance serving static files. When files are requested a user will receive a copy from the server closest to them, minimising latency.
A step down from that would be to use a more basic storage network like Amazon S3. When you upload a file to S3 it remains in a specific datacentre, rather than being distributed globally, so performance is worse. Although you won't necessarily see a performance boost from files uploaded to S3 vs your server, you can drastically reduce the load that your server has to deal with. Imagine you have a page with 30 images and 5 CSS & JS files. All of these could be hosted on a service like S3. Instead of your server having to process all of those requests when someone loads a page it only has to worry about the page markup itself. If your site has a large amount of traffic generating a lot of load, this can be the difference between staying up or going down.
Now if you simply serve your static files from a subdomain that's running on the same server as your site, you aren't going to see any benefits. All of the requests are still being routed through the same server - you are only making an aesthetic change.