Because they needed resources for industries
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Each country had their own reason for entering the war. Germany was pissed that they got screwed over by the Treaty of Versailles, Japan wanted to create an empire (at the expense of the "western" countries), Mussolini wanted to gain from France and Britain. Etc, etc.
With respect, Hitler's key territorial aim was to create a vast German empire in Eastern Europe. (There's no evidence that he wanted to revive the Holy Roman Empire).
she wanted to expand her empire
Arabs in the region wanted to gain independence from the Turkish leaders of the Ottoman Empire.
In the most simplest terms. The Japanese wanted oil and other resources and were not getting what they wanted according to their terms. Another reason was they wanted to rule the world. The Germans were led by Adolph Hitler who wanted to eradicate the Jews and all undesireables and he wanted to rule the European world.