The persuasion machine was a device that could control the beliefs of those it was used on, potentially enabling the universe to share a single ideology.
It was created in 1945 by the Nazi scientist Kurt Schalk, using information provided by the struwwelpeter. They were godlike beings from another universe, that believed this one corrupt. The persuasion machine was their method for "healing" it. To prevent the machine from falling into the wrong hands, Schalk used the machine on himself and his assistant Lukas Hinterberger to make them believe they were each other.
The Seventh Doctor managed to imprison the struwwelpeter. Meanwhile, Hinterberger (still believing he was Schalk) was taken by the Klecht entity, so the Doctor, Will Arrowsmith and Elizabeth Klein pursued him to prevent the persuasion machine being used. (AUDIO: Persuasion)
The Doctor located both Schalk and the persuasion machine being auctioned to several warmongering species by Garundel. So as to not make Garundel suspicious, the Doctor sent Klein and Will undercover to investigate the location of Schalk and the machine.
Returning to 1945 Minos, they discovered the Daleks had captured the real Schalk. The Doctor tracked them to the planet Azimuth. They finally confronted Schalk, alongside Davros, his "son" named Falkus (a clone of his younger self), and a squad of Daleks for control of the completed machine.
This was when Elizabeth finally discovered the truth of her existence — she had been bred in a lab during the final years of the Second World War to be the perfect control unit for the Machine. She was able to foil the plans of both Davros and his "son" by unwittingly convincing her biological mother, a cold-blooded high-ranking Nazi official, to replace her inside the Machine, which overloaded and was destroyed, killing her mother. (AUDIO: Daleks Among Us)