Bokmål (transl. Book tongue) and Nynorsk (transl. New Norwegian) are two written standards of the same language - Norwegian (norsk). People usually start with learning Bokmål because it's used by about 90% of the population while Nynorsk has a solid base in the western part of the country.
When it comes to pronunciation, that's a totally different story. Although there is a trend to standardise it, it's not quite there yet. This woman bot mostly tries to speak in Standard East Norwegian which is the unofficial spoken standard of Bokmål. Funny thing is that even native speakers will have some minor difficulties when meeting a fellow Norwegian who is not from their county.
All in all, although these standards and variations make it harder for learners to fully grasp the language, I think it's also great proof of how rich and diverse languages can be.
Both they are important to learn; the difference is both they raised in another places, so they have another words that we couldn't understand. Is like the english of USA and UK, and of course AUS. So, in Norway they usually use another languages of barbarians (only in their country). Hope you can undestand!