You can understand simply that dividing up a large computing resource (usually processing or CPU power) into little chunks which you can access remotely. This collection of servers on one location (data center) is called the cloud computing or cloud hosting super server.
Where
CDN is the content delivery network, here the same big group of servers divided into a small groups, and each group of servers installed in different locations across the country.
The CDN service is usually able to support much larger traffic volumes since the speed is calculated based on the nearest location of the server & the traffic comes from.
You can understand simply that a bunch of "servers" are spread across the world or country in different data centers. When you upload your file to one of these servers - and then tell it where your customers are coming from. It will then copy the same file to another server that is nearer to your customers; giving your visitors a faster experience. This collection of servers on different-different locations is called the content delivery network.
Cloud computing is usually used for large websites with high traffic but for small downloading because it used processing (CPU) resources where CDN is useful for large files and large downloading like video streaming, IPTV, etc. It uses high bandwidth than the CPU.