CDNs can improve the performance of your site by storing copies of your content at locations closer to your users. Services, such as the ones provided by Cloudflare, perform a MitM on your connection and save copies at data centers around the world. The difference from an unauthorized proxy is that you control the configuration, and you can purge the cache whenever you like.
You should be careful because if you don't use the caching features, then this can reduce the responsiveness of your site due to the extra hops involved. Make sure that you monitor the response times with and without a CDN, and you need a fallback plan in case they go down.
Another common use case for CDNs is to distribute popular libraries, for example, the jQuery ...
