Magic Swords. (Also here and here.)
In SM Stirling's The Sword Of The Lady, Chapter Seventeen, p. 523, Father Ignatius mentions Arthur's Excalibur and Roland's Durendal and Harberga mentions cursed Tyrfing. She is glad that the Sword sought by Rudi Mackenzie is not Tyrfing but what is it? How can mere possession of a particular sword make such a difference? The characters accept that this is the case because of a vision but I don't have visions! (My thought processes are verbal, not visual.)
While questing for the Sword, Rudi skirmishes with and weakens his enemies and also forges mighty alliances in every territory across the breadth of the former United States and the future Montival. Is this the significance of the Sword? It is at least part of it.
Poul Anderson never told us what became of Tyrfing.