This feature helps you to reduce the bandwidth between origin and CDN servers. Also, content delivery speed becomes higher because of reducing the time for compressing files in a CDN.
Enable Origin Pull Сompression to make a CDN pull already compressed content. Your server should support compression. CDN servers won't unzip your content even if a user's browser doesn't accept compression (actually nowadays almost all browsers accept it).
Note that this feature and GZip Compression exclude each other and don't work together.