Explanation: The mad Roman Emperor Caligula pissed off the commander of the Praetorian Guard, whose job it was to guard the Emperor. He would regularly denigrate the commander by calling him gay and a cuck, and being the Emperor, and a loose-cannon Emperor at that, the commander had to sit there and take it ~~like the cuck he was~~
For obvious reasons, pissing off your bodyguard is not a smart move; between the personal enmity and Caligula's own senseless reign, the Praetorian commander organized a coup which assassinated Caligula.
Caligula's uncle, Claudius, was a bookish man with a limp and a stutter who was largely kept around by Caligula and his court to torment with practical jokes. Once Claudius realized the Praetorians were butchering the Old Regime(tm), he suspected that being a victim of the regime wouldn't matter nearly so much as his closeness to it. Claudius hid behind a curtain in the imperial palace, having no other way out and hoping that he could survive just long enough for their wrath to subside.
Instead, he was discovered by a low-ranking Praetorian, who opened the curtain and recognized him as Caligula's uncle. Rather than killing him, however, this Praetorian saw an opportunity, whether ideological, practical, or... pecuniary. The Praetorian proclaimed Claudius Emperor, and rounded up some of his comrades to add their voices to the 'vote'. One expects that Claudius did not feel he had much choice but to agree if he wanted to keep his head attached to his body. An ever-growing crowd of Praetorian troops whisked Claudius away to their encampment 'for his safety' and spread the word of the new Emperor, even as unknowing Praetorian officers were arguing with the Senate over what to do next.
Claudius, who had remained reasonably popular even through Caligula's reign, was supported by the crowds, and so the Senate and Praetorian brass proclaimed him Emperor as well, seeing a fait accompli that would be hard to reverse. Claudius went on to rule as a reformer and deeply involved administrator who strengthened the Empire and the fairness of its legal systems.
... however, he never forgot what happened to his nephew. Not out of a sense of vengeance, as there was little love between the two, but out of... reasonable caution. So every year he paid the Praetorians a bonus multiplied by the number of years he was in power, as a celebration of the 'longevity' of his reign. The Praetorians remained loyal to him.
Money makes the world go 'round!