Spoiler alert. Stop here if you've not done the new heroics yet.
Arthas is holding back the Scourge from annihilating all of us. At first this makes no sense. He cut out his hard and it was destroyed. Tirion said there's nothing but a monster left. How could Arthas be protecting us if he has no good left in him?
Arthas the Lich King is not. He's trying to kill us. But Frostmourne on the other hand...
Arthas, the brave paladin who would sacrifice anything, even his own soul to save his people, he had his soul taken by Frostmourne. He's in there. And along with all the other souls, they may be able to restrain the Lich King.
This may also explain why Arthas would leave Frostmourne somewhere else. He may know that the blade is holding him back. But he cannot reject it or let it fall into other hands, for then he'd lose power. So he leaves it in the Halls of Reflection. As an added benefit, it acts as bait, luring in irritants like Jaina and Sylvanas where they can be destroyed or enslaved.
1 hour ago