Anon is correct. Palestine is NOT a nation, it was a region of the Roman empire.
The name was used by ancient Greek writers, and it was later used for the Roman province Syria Palaestina, the Byzantine Palaestina Prima, and the Islamic provincial district of Jund Filastin. The region comprises most of the territory claimed for the biblical regions known as the Land of Israel (Hebrew: ארץ־ישראל Eretz-Yisra'el), the Holy Land or Promised Land. Historically, it has been known as the southern portion of wider regional designations such as Canaan, Syria, ash-Sham, and the Levant.
After the Bar Kokhba revolt, Hadrian was so pissed that he renamed the area Palestine to try and eradicate any trace of the Hebrews. Earlier in the Roman empire the area was known as Judea, although names change depending on who is referencing the area.
There is no such thing as a Palestinian nation or people, everyone in that general area are primarily Arabs and Hebrews with a scattering of other ethnicities. They just use the Palestinian thing to try and stick it to Israel because they know they are the rightful heirs to the region and don't want to let them have it.