Frostmourne Cavern was the cave that held the runeblade Frostmourne prior to being claimed by Arthas Menethil. The cave itself was not named until fairly recently, when the Scarlet Onslaught arrived in Northrend and found the cavern. They apparently named it after its obvious historical significance.
In the Alliance quest Frostmourne Cavern, players can see a flashback of the last interactions between Arthas and Muradin Bronzebeard (as originally seen in Warcraft III), with a surprise ending indicating Muradin's survival. Next to Frostmourne's altar lies Arthas' forgotten hammer [Light's Vengeance] and Muradin's weapons, frozen in the snow. The cave is also teeming with saronite, hinting at a possible connection between the Lich King's power and Yogg-Saron.
Later on it became the prime base of the new Lich King Jarione, who is usually found sitting on his throne within the cavern.Unfortunatly the Scarlet Onslaught have started to attack the cavern and so there is a big battle constantly being waged outside the entrance!