I assume the OP wants to use a CDN to deliver static files like images/css/js via a CDN. This will allow those files to be delivered to the browser via edge cache servers, files uploaded to the CDN will be distributed to a global network of servers co-located with ISP's etc.
There are a few advantages, one being that these files are then usually served up a lot faster because of where they are served from, also some heat is taken off the users own web server. Sometimes if files stored on a CDN are accessed via a separate domain then that could also be cookie-less and the browser may be able to download more files in parallel, speeding up the overall page load even more.
In terms of how one would actually use a CDN in this way with Moodle, most CDN's would require some changes to be made to the code-base.
However, I've been using a service called CloudFlare recently which attempts to cache files by hosting the DNS zone for the site, making the set up a lot more straight forward.
CloudFlare automates most of the process and gives simple instructions for the bits that need to be set up manually. Once your DNS host is pointed to CloudFlare it will act as a proxy, serving static files from its own edge cache.
Because of the way CloudFlare proxies the requests to your server it also has many security features that can also help to improve site performance and reduce the risk of being hit by web spammers and botnets.
So yeah, I recommend CloudFlare!