Zionist ideas began thousands of years ago, but gained popularity in the late 1800s. Jews and Westerners supported Zionism because of anti-semitism. The video explains Zionism.
("What is Zionism?", "NowThis World" Youtube Channel)
After World War II, thousands of Zionists migrated to the then British Palestine mandate. Arabs opposed this, believing Zionists were stealing the land they had lived in for hundreds of years, causing conflict. The British received violent backlash from Jews after limiting immigrants. The UN split the mandate in 1947 into a Jewish state, an Arab state, and a UN-run Jerusalem to avoid conflict. Arabs resisted this. War broke out when Israel declared independence. No Palestinian state was set up. Tension and conflict, such as the Suez crisis, in the following 20 years led to the 1967 Six-Day War. Israel occupied territories belonging to Egypt.
"Israeli soldiers celebrating on 4 June" (The Guardian)
"French soldiers guard Egyptian prisoners on 13 November 1956 in Port Fouad during the Suez Crisis" (Middle East Eye)
After more hostilities, like the 1973 Yom Kippur War, newly-elected Jimmy Carter worked towards a peace agreement, based on UN Resolution 242. Carter met Middle Eastern leaders, encouraged by Anwar Sadat. Sadat wanted Sinai back, peace, and stronger ties with the US. Carter also met Menachem Begin. Begin was willing to consider Sadat's demands.
"Egyptian Troops Crossing the Suez Canal on October 7, 1973" (Times of Israel)
"President Jimmy Carter and Egyptian president Anwar Sadat at the White House, Washington D.C." (Library of Congress)
"Prime Minister Menachem Begin and President Jimmy Carter meet at the White House" (Center for Israel Education)
Sadat visited Jerusalem in November 1977, shocking everyone. Sadat addressed the Knesset, the Israeli Parliament, and Begin. They discussed the possibility of peace. Sadat's visit was bold, but a return visit was unsuccessful and no progress towards peace occurred.
"President Sadat addressing the Knesset during his visit to Israel" (Center for Israel Education)
Carter feared the halt in negotiations would lead to conflict. He wanted to capitalize on Sadat's visit. This led to him agreeing to Rosalynn Carter's brilliant suggestion to invite the leaders to Camp David, where seclusion could lead to an agreement. Carter wrote letters inviting the leaders. Both agreed.