Here's the chain of events you gotta understand. Forgive me if I get shit wrong, 'cause I'm really not a history buff. This is simplified ofc, I just want to give you a general idea.
1. After the Holocaust, a lot of Jewish people really wanted to have their own country to guarantee that they'd be free of persecution.
2. The UK happened to control the historical territory which used to be Israel, which by that time was populated by Arabs. Jewish people had been independently migrating to the area for some time. The UK and UN agreed to create an independent state of Israel, and Israel declared independence.
3. As Israel was established, there was a war between Israel and Arabs (both within the territory of Israel and nearby Arab countries). The Arab people inhabiting that land were forcibly deported and/or fled their homes, which were subsequently destroyed. They fled to Gaza and the West Bank, areas which are now collectively known as Palestine, and the people there are the Palestinians. 'Palestine' can also mean the whole country, but in contemporary politics, it's typically defined along ethnic and legal lines. Palestine doesn't belong to Israel, but Israel results various levels of military control over it.
4. Israel started building settlements in Palestine and continued the forcible removal of Palestinians.
5. Resistance movements in Palestine rose up. These movements ranged from crazed terrorists to secular independence movements. The Israeli government snuffed out the latter in favor of the former, believing the crazy terrorists would garner less international legitimacy and recognition.
6. The terrorist group Hamas would go on to take control over Palestine. That is the organization Israel is officially at war with.