Meteoric Weapons are the weapons that are rewarded after completing the secondary warden quests after reaching level 110. Inorder to get them, you must speak to Oisin the warden after completing the his first quest.
After accepting his quest, you must collect all the items he asks you too, this will include Remnants, Tablets, and a meteoric crystal. Those can be obtained by killing specific 6 Star Bosses, or buying them off other players.