This dagger has been on quite a journey. We first see it in season one when it's carried by the assassin who tries to kill Bran Stark, who is luckily stopped by Catelyn Stark (who fights him off with her bare hands, NBD). This is actually what sets off the War of the Five Kings, since Littlefinger tells Catelyn that the dagger is Tyrion Lannister's, and she goes on to take him hostage as payback (without realizing Tyrion actually lost the dagger in a bet and has no information about the assassination attempt). It's briefly seen in Ned's possession in season one, but disappeared after his death.
That is, until season seven's fourth episode, "The Spoils of War." It turns out Littlefinger has had the dagger all along and gives it to Bran as a peace offering of sorts. He in turn passes it on to Arya, who will no doubt get way more use out of it.
