To not heat up or add to the resistance of a coil, this type of wire is usually prominent in coilheads where the leads should not heat up and are longer then other coils/connections.
The original use of the NRN wire was for the Golden Greek (GG) atomizers like the Penelope and Ithaka. They required the wires run down the sides of the atomizer to the contact points well BELOW the deck. You only wanted Res wire where your actual coil was, over the air flow in the ceramic cup. They are a bit of a pain to make, and were Kanthal for the res, Ni200 for the NR.