Well it is pretty weird and unclear. There are various versions of the saga that approach the topic in different ways.

The most likely, I believe, is that it is some sort of reference (real or mythological) to the genealogy of Gunnar (or Gunther), an early 5^th century king of the East Germanic Burgundians during the destruction of the Burgundian kingdom by Attila (or German Etzel) and his Huns.

In the Poetic Edda, Niflungar is used several times to refer to both Gunnar himself and his treasures, although other, mostly later, sources use the term Nibelungen to refer to a race of dwarves (sometimes also featuring giants), which is what Richard Wagner famously went with for his Ring Cycle.

In any case, we can say that one Nibelung "dynasty" did really exist, as a branch of the Pippinids and Carolingians. The illegitimate son of Childebrand I., brother of the Duke and Prince of the Franks Charles Martel, was named... Nibelung (~700-780 or something in that area) and several of his descendants were named Nibelung as well, although the genealogy is a bit unreliable. See here.