Harry sat and thought for a moment how best to explain it and then just settled for shrugging and said, "Basically."

He moved his bishop.

"Pureblood supremacy's been a thing with with some wizards for a very long time. With others, blood status is nonsense, and they think, rightfully so, that nonmagical people should be left alone, that they're not inferior to wizards. Right now, though, there's a leader to rally around, a very dark wizard by the name of Voldemort. He's not even a pureblood himself, but none of his followers know it--they probably wouldn't believe it."