The All Thing is a consensus-based public forum accessible to all members of the Hegemony via neural implants (comlogs). It was a real-time network which governed Hegemony politics, fed information to tens of billions of data-hungry Hegemony citizens, and that had evolved a form of autonomy and consciousness of its own. If one considers the Hegemony of Man as a bi-cameral form of government, the All Thing would be the "lower house" - the Senate being the "upper house". For instance, the All Thing was led by the Speaker of the All Thing (analogous to Old Earth's United States' Speaker of the House). It had media representatives that fed images and infomation to the billions of people. The TechnoCore participated in the All Thing via its AI Advisory Council.
Estimates said the All Thing dealt with around a hundred active pieces of Hegemony legislation per day during the Web Era, which were discussed on debate channels. Citizens were able to vote on legislation every few minutes if they wished. Millions of people around the Web had a sort of "addiction" to the All Thing "like slugs". Its existence depended on farcasters and via fatline and was maintained by AI management of real-time Swarzschild patterning.
The All Thing was responsible for approving the Seven Pilgrims to the Final Shrike Pilgrimage. It was also responsible for saving the Wraiths, lifeforms native to the ice world of Sol Draconi Septem, after much lobbying by the Templars, by stopping the project to heat up the northern reaches of that world.
The term "All Thing" is derived from the Alþingi (anglicised as Althing or Althingi), the national parliament of Iceland and one of the oldest extant parliamentary institutions in the world, founded in 930 C.E.
SPOILER ALERT! The section(s) below are MAJOR SPOILERS.
The All Thing simply ceased to exist after the Fall of the Farcasters, as all of the Web worlds were no longer connected in real time. In consequence of the descruction of farcasters, the connections among the dataspheres of hundreds of worlds was severed in a matter of seconds, thus making it impossible to maintain the forum.