The Fatline is an instantaneous communication technology. The term is likely a contraction of "Faster Than Light Communication Line," or some similar phrase.
Fatline is capable of transmitting holographic images as well as 2D videos over interstellar distances in an instant. Fatline is the basic means of communication in the Hegemony. The protocol and the equipment is created by the TechnoCore, but the Ousters also were able to produce their own equipment based on the same principles - they called it the "Void Which Binds".
Fatline technology utilizes tachyons as it's transmission medium - faster than light particles sent in a burst that decays over time and distance. This burst of decaying tacyons must be converted and decoded by a receiver at the destination.
SPOILER ALERT! The section(s) below are MAJOR SPOILERS.
During the collapse of the Hegemony, Meina Gladstone sent out a mass fatline broadcast to every receiver within the Hegemony - a message with "a transmission value of several hundred million gigaelectron-volts" - in order to make the Hegemony aware of the TechnoCore's deception and its role in the assault on the WorldWeb. Almost immediately following this, all fatline traffic ceased abruptly, followed by another mass fatline broadcast from an unknown source:
"THERE WILL BE NO FURTHER MISUSE OF THIS CHANNEL. YOU ARE DISTURBING OTHERS WHO ARE USING IT TO SERIOUS PURPOSE. ACCESS WILL BE RESTORED WHEN YOU UNDERSTAND WHAT IT IS FOR. GOODBYE."
It was widely believed that this message had originated from the TechnoCore, as no other entity or group of entities was known to possess power over the fatline communication medium. However, it was later revealed by Aenea that the message had in fact been sent by the Lions and Tigers and Bears, powerful sentient entities residing within The Void Which Binds.
- Hyperion, 1995. Prologue, pg. 3.