Krasko was a mass murderer imprisoned in Stormcage Containment Facility (WC: Case File Three) in the 52nd century. (COMIC: The Master Plan) He murdered around 2000 people and revelled in his crimes, but Stormcage punished him by installing a neural restrictor into his brain, which stopped him from inflicting harm or killing any living thing, no matter how much Krasko wanted to. (TV: Rosa)
Using a vortex manipulator, he travelled back in time to change history.
The Thirteenth Doctor, Graham, Ryan and Yaz encountered Krasko in Alabama 1955, after finding a suitcase filled with time displacement equipment. He wanted to change history by meddling with such small events that would prevent Rosa Parks from refusing her seat and starting the Montgomery Bus Boycott.
Krasko's plot was averted by the Doctor and her companions who managed to ensure Rosa began the boycott, no matter what he tried. Krasko's vortex manipulator was destroyed by the Doctor, leaving him unable to time travel. As Krasko finally attempted to stall the bus on Rosa's route, Ryan used Krasko's own temporal displacement weapon, to send him as far back as he could set the device for, presumably forever stranding Krasko in the distant past, (TV: Rosa) likely the age of the dinosaurs, according to Yaz. (WC: Case File Three)
Krasko's racism led him to believe that "things started to go wrong" with Rosa Parks' victory. He told Ryan that "[his] kind would be put in [their] place". He was sadistic as he showed no remorse for the two thousand people he had murdered and when recalling his crimes to the Doctor, he smiled with pleasure. He also made a joke about not really remembering how many people he'd murdered.
Because of the restrictor in his brain stopping him from inflicting pain or killing other people, Krasko was visibly frustrated when the Doctor snatched the vortex manipulator from his wrist and stomped on it, not being able to strangle her when he managed to overpower her briefly.
He also didn't care about the Laws of Time and what could happen if Rosa Parks did not make her historic victory.
He was able to blend in while in 1955, dressing in the appropriate fashion as not to raise suspicion.