The Imperius Curse is one of the three Unforgivable Curses in Harry Potter. Specifically, it's the one that allows the caster to essentially control every aspect of the person being cursed, turning them into a human puppet. The spell was commonly utilized by followers of Voldemort, and could be used to gain information and even carry out murder. So what's all that got to do with Arthur Weasley? Throughout the series, most everybody perceived as good hates the Malfoys. They're known to be vicious, conniving and it's practically common knowledge they were/are in strong alliance with Voldemort. But none seem quite as all-consumingly bitter as Arthur Weasley. Despite the fact that nobody ever talks about Voldemort in the wizarding world, Ron is able to tell Harry all about Malfoy's father's acquittal after Voldemort's disappearance (this while not having a basic enough knowledge of the situation to know what the Dark Mark is). The theory puts forward that Arthur was trialled for his crimes while under the curse, and that he got off on the same acquittal that Lucius did, even though Lucius was genuinely on Voldemort's side. Later, when Moody is teaching Defence Against The Dark Arts, Ron is able to name and describe this curse, telling Moody that his father told him about it. Moody is interested to hear this, and tells Ron that it makes sense his father would know it. This would also explain why Arthur was never able to rise any higher in the Ministry, despite his long and esteemed service.
