As a form of territorial governance, the nation-state emerged in Western Europe some time during the last 1000 years. Just when and where depends, of course, on just what you think qualifies as a nation-state. I note, for example that at the time of the French Revolution, most of the people in that territory did not speak French. Was it a nation-state?
The question of Palestine has made the issue an acute one, but:
The Montevideo Convention on the rights and duties of states, signed by 20 countries in North and South America in 1933, sets four criteria for becoming a state: a permanent population, a government, defined borders and the capacity to enter into relations with other states. But these are little more than guidelines. Many places recognised as states do not comply. Libya has more than one government. Many states emerged after national movements declared independence and then sought recognition by other states and admission into the United Nations. Yasser Arafat, the leader of the Palestinian Liberation Organisation (PLO), declared Palestine a state in 1988 in Algiers, and has subsequently secured recognition from over 130 states, or over two-thirds of the UN.