To give a little more depth from what TED notes, this did take shape over time and was based on Zionism and how it was being viewed by the British at the time. There were also competing interests that eventually collided as time wen on. When the Ottoman empire entered on the side of the Germany this prompted Britain, France and Russia to partition the Ottoman territories in the event of an Allied victory. The British pledge to Sharif Husayn of Mecca and the Sykes-Picot Agreement between Britain and France were two of the principal proposals for territorial division. The Balfour Declaration was another, yet it was met with suspicion by France and Sharif Husayn as contravening the agreements Britain had already made.
During WWI it was widely believed by many within the British government that Jewish groups held an unusual amount of power within the Russian and American governments. This might affect Russian and US involvement in the war and until the American declaration came it was thought that Germany might make a declaration of support for Zionism and then America might enter on the side against Britain. With Russia being unstable it was thought that it too might be swayed by any German sympathy towards Zionism. So it was thought that British interests would be served by gestures of goodwill towards the Zionists, Chaim Weizmann was the spokesman in London during this period and was a significant policymaker, he was also a very charismatic spokesman and had many ties within the British government. He kept the idea alive about a Jewish Homeland in Palestine, it should be noted that what the Jews thought of as a homeland and what the British considered it as became the main point of contention later on.
British strategic interests in the Middle East were helped out by promoting the Zionist cause, this gave them an ally in the area and would also keep out France. The Balfour declaration gave the British support for Zionism, yet it was ambiguous and contradictory enough that later on this would be hard to implement and was chiefly a failure as the competing interests noted here did not get what they wanted. The idea that you could grant a Jewish state and provide for the continual rights of the non-Jews in the area was not possible as written. When the British captured Jerusalem in December 1917 this allowed for the British military occupation of Palestine and it was then that the British tried to reconcile Zionism and Arabism by getting Weizmann and Faysal of Syria to negotiate. They did agree to cooperation between the Jews and the Arabs so that Jewish communities would cooperate with the Arabs and Faysal would recognize the Balfour Declaration and consent to Jewish immigration so long as the rights of Palestinian Arabs were protected and Greater Syria was independent. Faysal did not agree to a Jewish state though, this becomes important later on. Although, once the French took Syria these agreements became null and void.
The main point became the idea of a Jewish national home, Weizmann was sure what it meant as a spokesman for Zionism, he had stated at the Paris Peace Conference that the Zionist objective was to make Palestine as Jewish as England was English. The Zionists expected the British to go along with this idea, Britain did not and within the Balfour Declaration had noted that they wanted to protect Palestinian Arab rights as well. It was the idea of equal obligation and the unsolvable contradiction to the Balfour Declaration. The British tried to clarify itself in the 1922 White Paper, and within there noted that a Jewish nation home did not mean imposition of a Jewish nationality on all of Palestine. It did note that Jews had a right to be in Palestine and that it should become a place where the Jews could go. Yet the British High Commissioner tried to balance the Zionist aims and the freedoms of the Palestinian Arabs, yet failed and it was through this that the Jews and Arabs became hostile to each other. This was exacerbated once Jewish immigration raised the population representational ratios from about 82-16 Arab-Jewish in 1931 to 67-31 Arab-Jewish in 1946. Land was bought by the Jews from absentee Arab landlords such that the Arab tenant farmers were evicted, which began a cycle where Arabs were becoming economically depressed (considering this was the 1930's) and began having to sell land, which increased Jewish land ownership. This also dispossessed the Arabs where they considered themselves as unrepresented from their own leaders, the British were seen as not being willing to intervene and the Zionists they considered as the cause.
With this antagonism building due to immigration and land purchases, tensions rose and the Arabs protested with acts of violence with the Wailing Wall disturbance of 1929 and revolts within 1936-1939. This is when the British responded by first the Shaw Commission which noted that Arab rights were not being protected as per the Balfour Agreement and that Jewish immigration needed to be put under British control, instead of following these recommendations the British then sent the Hope-Simpson Commission and their recommendations were put into the Passfield White Paper which finally stressed British obligations to Arabs and Jews and it was a recommendation here that Jewish immigration needed to be restricted due to the limited economic capacity of Palestine.
Sorry for the long background, but this is a complex situation that took time to build up, and although this was eventually overturned by Weizmann and members of the British and US governments it was at least a point where the British really tried to clear up their own inconsistencies and policies in the region. My main source for this was A History of the Modern Middle East by William Cleveland and Martin Bunton, we used this text in my Modern Middle East History class and it is very thorough on this situation.