Arthas was the former prince of Lordaeron, as well as a former Paladin on the Silver Hand Paladins. After the Plague was released he fought to save his people but eventually became obsessed to insanity with it. Eventually having the city of Stratholme razed and it's inhabitants killed to "save" them from the plague.
He traveled to Northrend in pursuit of Mal'Ganis when he came across Frostmourne. The rest is history