During WWI, the British were at war with, among others, the Ottoman Empire, which controled Palestine. The British, at that point, put out the Balfour Declaration, in which they declared their support for a Jewish state in that area. They did so in hopes of getting people in Palestine on their side in the war. They also hoped that would make the area easier to govern after the war.
WWII, of course, brought the Holocaust. This was the major reason behind the creation of the State of Israel. The West felt that Jews should have a nation of their own so as to be less vulnerable to anti-Semitism. This led to the creation of Israel in 1948.
The creation of Israel, of course, led to many of the problems that now exist in the Middle East, with Arab nations very unhappy with the existence of Israel and with the constant support the US gives Israel.