Hearing about the Two-State Solution for the mess in Gaza and Israel made me wonder why Palestine was made to be no longer a state in the first place despite it still apparently having land by the old borders.
Well, Palestine has actually never existed as a state in history. Israel was not carved out of Palestinian territory, Israel was made of partitioned British land. After the dismantlement of the Ottoman Empire in WWI, its Middle Eastern territories where granted to France and Britain. France was given Lebanon and Syria, and Britain was given Palestine, Jordan, and Iraq. These were territories with the moniker of "mandate". They were territories that would eventually be granted independence when it is felt they could function as independent states. After WWII, in 1947, the UN made a plan to partition the British mandate of Palestine into 2 states, Arab and Jewish. Here would be a good to time to clear something up also. The land of Palestine which has encompassed the area now known as Israel and it's territories, gets its name from an ancient group of people, the Philistines. The name Palestinian for the modern day Palestinians evolved in the 20th century for its Arab inhabitants.
The UN Partition Plan was approved by the members of the UN with the Arab nations notably voting against, and the plan was given to the United Kingdom as the plan for the independence of the Mandate of Palestine. When the UK put the plan into action, Israel declared its statehood. A coalition of Arab states declared war on Israel to end the Partition Plan. Israel won the war and acquired the borders it would have until 1967. The Arab state never came into existence as Gaza was annexed into Egypt and the West Bank was annexed by Jordan.
Following the Suez crisis, tensions returned and Arab forces gathered on the border of Israel in preparation to invade. Israel launched a defensive preemptive strike thus starting the Six Days War. Israel would win and take Golan Heights and it took over administration of Gaza and the West Bank. Israel also retook the Sinai Peninsula which it shortly held after the Suez Crisis. In 1973 the Arabs launched on surprise attack on Israel on Judaism's holiest day, starting the Yom Kippur War. The Arabs hoped to reverse Israeli gains from the Six Days War, but they were repulsed. Israel would later return the Sinai Peninsula to Egypt in a peace treaty, while Egypt demilitarized it and recognized Israel. This is how the current borders of Israel were formed.
I answered almost word-for-word this question in this post.
Quite frankly, that'll cover everything you're looking for, I'd think.