Compression is a simple way to optimize your website in terms of speed and page rendering. CDN is either able to deliver already compressed content if your origin server supports it, or use the compression on the side of CDN.
The compression policy usually allows to give the list of file extension of the files that CDN has to automatically compress before delivery to the end user. Such method is usually used if the origin does not support compression or you cannot modify it accordingly to tune up compression. After you specify the needed file extensions that should be compressed and the file with this extension will transmit to CDN, the certain parameters will be checked. If they contain Gzip or any other sign that the client may work well with compressed content, then the CDN server will give the compressed version of the file.