Hitler felt he needed to take Norway for several reasons. One was for control of the North Sea. Norway would provide Hitler ice-free harbors for his navy and airfields for his Luftwaffe which he would need in the Battle of the Atlantic. Britain knew this and was already planning to put bases of their own in Norway, so therefore, Hitler had to invade before Britain could do that.
Hitler also needed to make sure that Sweden couldn't sell their iron ore to anyone other than Germany. If he were to invade Sweden, it would cost him dearly in terms of troops and resources. But by isolating Sweden, including their overland trade route to Norway, then he wouldn't have to take Sweden until after he conquered the rest of Europe.
Norway tried to remain neutral in WWII like they did in the first world war. But on 9 April 1940, Hitler invaded them without warning. The under-prepared Norwegians did put up a good fight and, for a while, the British pitched in and helped them. However, the British had to start pulling out when the Germans invaded France and the low countries on 10 May. The stronger German forces wore down the smaller Norwegian military and on 10 June 1940 they were forced to surrender.
But the Norwegians weren't done in. A large number of ships in both the Royal Norwegian Navy and merchant marines were able to avoid capture and joined the Allies. Norway was able to provide the RAF with four fighter squadrons. By the war's end, some 28,000 Norwegians who were able to flee Norway enlisted with the British forces.
For those who couldn't get out of Norway, many joined the Norwegian Resistance. These people were able to create all kinds of problems throughout the war. Among their many heroics, they sabotaged Germany's atomic research plant (heavy water). Then as the Nazis were moving it back to Germany, the underground sunk it while crossing a lake. This ended Germany's quest for the atomic bomb.
Another advantage for the Allies was the fact that in order to hold Norway, Hitler had to keep 300,000 troops stationed there. Did these 300,000 men hold Norway or did Norway hold them? This was 300,000 men who could have made a big impact somewhere else but were stuck there for the entire war.