The Norse Sword is a very fast dual-edged sword that has good reach and thrusts but limited cutting power.
The most effective attack with this weapon is stabbing; slashing and overhead attacks are largely ineffective, but can be used to finish weak enemies.
Since stabs must be aimed relatively accurately to hit mobile targets, this is one of the few weapons which benefit from using a first-person perspective while playing. This can be further complemented by the use heater shield (whose shape minimizes visibility loss while guarding) or a throwing weapon for obvious reasons.
It is actually one of the longest pure 1handed weapons in the game alongside the Broadsword; beaten only by the Morning Star. With the Cudgel, they both share the same reach. This combination is useful if you like to have both sharp and blunt weapons with safe distances.
The Norse sword used to be a stab dedicated one-hand sword back in early release of the game, although it was seen as too powerful and was nerfed, now today The Norse sword serves as a faster alternative for one-hand swords.
The description says that The Norse sword is a dual edged sword that has good reach and thrust damage, but limited cutting power. As for now, the information seems to be the opposite due the balance fix, description has not yet been corrected.