The Palestinians are the Arabs who live (or used to live) in the same land that the Zionist Jews now live in. They are primarily descendants of Ishmael, who is the first physical son of Abraham. It was Hagar, a handmaid of Abraham's wife Sarah, who gave birth to the child.
Some of the modern-day Palestinians are also likely descendants of Lot (one of Abraham's relatives whose two daughters gave birth to the peoples of Moab and Ammon) and Esau (one of Isaac's sons and brother of Jacob).
Although the Palestinians are in Abraham's lineage, they were not given the same blessings and inheritance as Isaac. Although Isaac was Abraham's second son through him, he was the only son produced between himself and his wife Sarah.
God himself declared that Isaac would inherit the birthright blessings which included Canaan (Genesis 21:10 - 13, 17:6 - 9, 15:16 - 21 and so on). The Lord still blessed Ishmael, the father of the Palestinians, but not to the degree as Isaac (Genesis 16:10 - 12).
Many of the Palestinians have not lived in the land for generations but moved to it after the Zionist movement's economic development created jobs for them. The 2005 World Almanac states regarding the land that "Jewish immigration, begun in the late nineteenth century, swelled in the 1930s with refugees from the Nazis; heavy Arab immigration from Syria and Lebanon also occurred" (page 789).
The famous 19th century writer Mark Twain, living during the time the Ottoman Empire ruled what we now call Israel, remarked how sparsely populated this area was and that it was a desert.
Jewish settlers bought land in Palestine during the British Mandate period and after the Balfour Declaration (which said that the British government was in favor of creating a homeland for the Jews) came into existence in late 1917. This was long before the Palestinians and their rights became a global issue. It was only after these settlers began to improve the land they bought that many Arabs from other locations moved into Israel as well.
The nation of Israel occupied, in 1967, areas known as the West Bank (including East Jerusalem) and the Gaza Strip after its decisive victory in the Six-Day War. Although the Palestinians argue these areas belong to them, and wish to use them to form a future state of Palestine, Israel maintains control of them to this day.
Here is something interesting to consider regarding the Palestinians and their conflict with others. If the existing Arab regimes in the area took in their fellow Arabs and Muslims after 1948, and let them assimilate and immigrate among them, granting them full citizenship, a good portion of the mess we see today in the Middle East would not exist.
Put another way, if the Arab world really treated the Palestinians as their brothers, they would have let them resettle among them. This type of merciful act has occurred in recent history. It happened when India took in Hindus from Pakistan as well as when the nation of Israel took in Jews from the rest of the Middle East.
In summary, the modern-day Palestinians are the Arabs who used to live or who live today in the modern State of Israel, including the occupied territories such as the West Bank and the Gaza Strip. They are primarily the descendants of Ishmael, Abraham's oldest son. Although some have been in the Holy Land for generations, many have not.