Britain was awarded a mandate, by the League of Nations, to govern Palestine after WW1 upon the dissolution of the Ottoman Empire. Britain also had a mandate to govern the Transjordan and Iraq. France was awarded a mandate to rule in Syria and Lebanon. This is what is refered to as the Mandate System
Look up Sykes-Picot Agreement of 1916, T.E. Lawrence, Hashemite dynasty, mandate system, etc. all available on Wikipedia....
The State of Israel was declared on May 14, 1947 the day before the British mandate was to end.