There were numerous effects of the Holocaust in building both the Jewish State of Israel and the Arab opposition to it. The following are the three most important of them.
State of Israel: This is probably the most common answer. The Zionist project existed long before the Holocaust. (The first Halutzim came to the territory of the British Mandate of Palestine while it was still under Ottoman control -- late 1800s and early 1900s and Ze'ev Jabotinsky encouraged Polish Jews to immigrate to the British Mandate of Palestine in 1937.) However, after the Holocaust, it became clear to the International Community that the Jews needed a place to exist freely and without fear of persecution where previously this sentiment was confined to radicals in the Jewish community. (Most Jews were anti-Zionist or at least not pro-Zionist before the Holocaust.) As a direct result of the Holocaust, the United Nations convened and proposed the UN Partition of the British Mandate in 1947 which gave Israel a legal claim to statehood in 1948.
Nazification of Arab Nationalism: This is usually glossed over, but the root causes of the Holocaust like the Nazi ideology were important in the development of Arab Nationalism. During the Colonial Period in the Arab World, the Arabs felt that while they were the sons of conquerors who ruled vast empires, they were now humiliated and conquered by the British and the French. This feeling of subjugated superiority matched the Nazi profile and as a result, Arabs began pilfering Nazi doctrine and adding it to their own Nationalist sentiments. This caused Arab Nationalism to have a more militaristic and violent character in addition to giving it a more anti-Semitic character. Pogroms and violent persecution of both Jewish and Christian minorities ensued, especially in nations that had direct dealings with the Axis Power like Iraq. The legacy of the Nazification of Arab Nationalism is still quite strongly ingrained in the Arab World.
Mizrahi Jewish Exodus: Because of the two above results of the Holocaust, the overwhelming majority of Jews who lived in Arab countries were forced out of their homes or felt compelled to leave to avoid further persecution and went to Israel, France, the United Kingdom, the United States, and Canada, in addition to other regions. The amount of Jews in the entire Arab World in 1945 is over ten times the number in 1975.
It is also thought to have accelerated the process, arguably it would may not have happened without the Holocaust.
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To add to the other answer, before the Final Solution, Hitler attempted to exile the Jews out of Germany. One such place was Palestine. Hitler cooperated with the Zionist Movement to successfully exile the Jews.
They died.
it affected them by the nazi starting the holocaust
Zionism did not affect the Holocaust. The Nazis were anti-Jewish in a racist sense. They didn't draw any distinction between practising and non-practising Jews, or between Zionists and non-Zionists. On the other hand, it is often said that the Holocaust had the effect of strengthening Zionism.
Israel was a colonial possession of the United Kingdom. The Israelis were in their own mess during World War 2. They had to do what the Brits wanted them to do and they wanted their own freedom. Once World War 2 was over they did fight the Brits for their independence in 1948. I have given you a link below that you can read.
Germany