Palestine is the term used today for territories including Israel and Jordan, using the modern reference that takes the landscape of Ancient Palestine into account. The word itself comes from the Hebrew Peleshtim, or Philistine, which itself may have originated in texts from Egypt.
There is a great deal of controversy about the boundaries of Palestine, whether it encompasses all of the area west of the Jordan River, or if any of its history should be used as a modern rubric for restoration of lands. The only certain thing about the history of Palestine is that it is constantly being debated and redefined.
However, a few things about its early history are known for certain. For example, as mentioned, it is generally accepted to be west of the Jordan River, and may extend to the Mediterranean Sea. The Ancient Palestine tribes were, at one point, controlled by the Assyrian Empire, and the whole area was variously controlled by Christian, Muslim, and European interests for most of its recorded history. Additionally, the entire region contains many sites of religious significance to many religions.
The links below should provide a very good overview of the conflicting opinions, facts, and history of the Palestinian areas. In a topic as conflicted as this, all claims should be sourced and fact-checked to the best of your ability.
The complete history of Palestine would, of course, take at least a few books to write. Here, I will attempt a very brief overview of the last 100 years or so of the area's history.
Before WWI, Palestine was part of the Ottoman Empire. That empire was destroyed in WWI and Palestine was given to the British to administer. Early in the 1900s, Jews started moving to Palestine with the start of the Zionist movement. This movement was given a boost by the Balfour Declaration, in which Britain promised to help create a Jewish state in the region, but one that would not take away the rights of any other groups. During the time of British rule, there was fighting between Jews and Muslims for power as well as between Jews and the British as the Jews wanted a quicker establishment of their own state.
After WWII and the Holocaust, the Western powers set up Israel as a place for the Jews to live so they would not be susceptible to anti-Semitism. Over the next decades, there were repeated wars between Israel and its neighbors. The Arabs who had been living in what is now Israel mostly left or were forced out. Ever since then, there has been conflict over the desire of these Arabs (called Palestinians) to have their own state.
Right now, most people on both sides agree that there needs to be a "two-state solution" in which there is both Israel and a Palestinian state. But there is yet to be any agreement on how this will come about.
Please follow the link below for a much more thorough discussion of this subject.