Amazon calls it CloudFront, and it costs $0.17 – $0.22 per GB at the lowest usage tiers. It seems that you simply put your files in an S3 container, make an API call to share them, then let your users enjoy the lower-latency, higher performance service.
Their domestic locations include sites in Virginia, Texas, California, Florida, New Jersey, Washington, and Missouri. Internationally, they’ve got Amsterdam, Dublin, Frankfurt, London, Hong Kong, and Tokyo covered.