The Thaumic Reactor is a massive reacting engine designed by Ponder Stibbons to split the thaum and generate massive amounts of magical energy in the process of thaumic fission. It was built on Unseen University's squash court, a place where the walls are designed to teleport incoming objects (such as squash balls) to other walls. Nothing excites a particle like meeting itself coming the other way, and this is something he should have taken into consideration...
It was mostly developed by Ponder, but he was inspired by the Scrolls of Loko, where a previous attempt at thaumic fission created a very deep valley surrounded by a ring of mountains. A lot of curiously shaped magical creatures can be found there. And an expedition led by Stanmer Crustley contracted serious magical diseases a few months after returning (Crustley died of planets), but they did manage to recover the scrolls.
With this in mind, Stibbons built in some safety measures to the reactor. The fail-safe device is the Bursar, who he got to stand with an axe next to a rope holding up a lead rod laminated with rowan wood over the center of the engine. If things get out of control, he would chop the rope and the rod would fall, and shut down the reactor- as rowan and lead naturally dampen magical reactions. Bearing in mind the Bursar's temperament, the back-up fail-safe device was Adrian Turnipseed, who stood next to the Bursar and whose job it was to shout "For gods' sake cut the rope now!".
It took three years for the University Council to approve Stibbons' request to build it. His suggestions that it would push back the boundaries of human knowledge or make people much more happier were ignored, but finally he suggested that it could be used to generate a lot of cheap heat, and they allowed him to spend AM$ 55,879.45p on it, since the dwarfs charge the University very high prices for coal and many of the senior Faculty have rooms on the colder side of the university.
Because of this desire for warm rooms, the wizards agree to activate it in The science of Discworld, even though there is a slim possibility that it could blow up everything- the entire Disc and everything within a radius of fifty thousand miles out into space. And despite the fact that the energy it could generate would be powerful enough to send the University to the moon.
Within a day of it being activated, the Bursar wanders off and the engine generates far too much magic, turning the university into "a baking desert under a flamethrower sky". The wizards desperately need something to do with all the excess magic (less it rip a hole into the Dungeon Dimensions), and Ridcully approves a plan to use the magic to create the Roundworld project. Despite the Dean's protests that it would take months, Hex is able to create the project and use up most of the magic from the reactor in less than a minute.
When the time comes to deactivate the reactor, as all the magic has been used up, Ridcully tries to get Rincewind to do it (by redefining the danger of going inside the squash court as "not as dangerous as some other things"). But Rincewind is saved when the Bursar, whose mind has been destablilized by trying to understand a Hex readout about Roundworld physics, goes in and plays some squash. In the process he deactivates the reactor and catches Uncertainty. Uncertainty being a nasty thaumic disease that causes the brain to forget where it is whenever it remembers who it is.
Sometime after this, Ponder ties the reactor to Hex, allowing him to activate and deactivate it will, and turns it back on. However, Ridcully forbids Stibbons to run it at anything near full power. This means that the wizards have no way to physically enter Roundworld (outside of virtual suits operated by Hex), as it would require a massive amount of magic. So, when in The science of Discworld II: The Globe, Stibbons,Rincewind, and the Librarian need to get in to help fight the elves, they need to use L-space.
During The Science of Discworld III: Darwin's Watch, Ridcully demands a campaign map in the wizards' fight with the Auditors of Reality. So, Ponder gets Hex to "resolve a thaumatic glyph in conditional Darwin space". This basically means creating a three-dimensional map of where wizards need to be sent to put things right- where "nodalites" need to be resolved so that Darwin writes the Origin of Species, not the Theology of Species. To do this, he needs to run the reactor a "little higher" than normal- at about 200% percent.