How Dial-up Acceleration Servers Work:
An Illustration.

(Click here for the full explanation on "Speeding Up Your Modem")

Legend for illustration below:

Blue = compression-acceleration servers (aka "proxy servers")
Green = web page content, compressed and uncompressed
Red = your current ISP, who now received compressed content via the proxy servers.

(More: click here for the full explanation on "Speeding Up Your Modem")