The Palestinians are simply 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, the first physical son of Abraham (through a handmaid named Hagar). 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 - Israel).
Although the Palestinians are in Abraham's lineage (through Ishmael), they were not given the same blessings and inheritance as Isaac (the son of Abraham and Sarah). Isaac, although Abraham's second son, was the only son he had with Sarah his wife and the child through whom God himself declared would inherit the birthright blessings (which included the land of Canaan - see Genesis 21:10 - 13, 17:6 - 9, 15:16 - 21, 22:17 - 18). God still blessed Ishmael 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 says 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).
During the time of Ottoman rule the writer Mark Twain, when traveling through the Holy Land in the 19th century, remarked about how sparsely populated this area was, as it had become a desert. However, as the Jewish settlers improved the land that they had bought during the British Mandate period after World War I and the Balfour Declaration (which said that the British government was in favor of creating a homeland for the Jews in what is now modern Israel), many Arabs from other locations moved in.
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. In other words, if the Arab world REALLY treated the Palestinians as their brothers, they would have let them resettle among them, just as the Indians took in Hindus from Pakistan, Israel took in Jews from the rest of the Middle East, and so on.
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. Some have been in the Holy Land for generations, but many have not, having moved in after the Zionist Jews came into the land.