During the late middle ages and up to around the 1800 the Scandinavian languages were hugely influenced by Low German and Dutch. So much so, that our languages today are somewhere in the middle between Old Norse (which has been largely unchanged on Iceland and the Faroes), and Dutch/Low German.
The scandinavian languages today are what you may call creoles (a mix) between Low German and Old Norse.
Danish is the language that had the strongest influence from Low German. Some Norwegian dialects however, kept more vocabulary and structure from Old Norse. In the 1300's Norway fell under Danish colonial rule. Denmark imposed their language and culture on Norway, and over time the aristocracy and burgouise developed a form of Danish with Norwegian accent and some Norwegian loan words. This is the language that formed the basis for Bokmål, which became the dominant language in Norway.
However in the 1800's, self tought linguist Ivar Aasen embarked on a grand project to collect samples from all different Norwegian dialects, which had diverged greatly because of the lack of a written standard language under Danish rule. He used the dialects of Indre Sogn, Hardanger, Valdres and Hallingdal as the backbone of a new written language, because they had retained a grammatical and phonetical consistency from Old Norse, however much simplified. To create a unified language for the whole country, he added words from all the different dialects he had sampled, from the north, east, south and west of Norway.
Unfortunately, by the time Aasen had formed his Language, Bokmål was already becoming the leading language of newspapers, commerce and politics, especially in the larger cities. The old elites with their cultural ties to Denmark held on to their power and successfully supressed the attempt to unify Norway under a language based on Norwegian dialects.
A small group of people are now trying to revive Ivar Aasen's original language, called Høgnorsk.