The flag of Palestine is three horizontal stripes, black over white over green, with a red triangle at the hoist.
From the Arab Revolt to the PLO
The design descends from the flag of the Arab Revolt against Ottoman rule during World War I. A version with the same colors in a different arrangement appeared in 1917 as a banner of Arab nationalism, and through several iterations it attached itself specifically to Palestinian nationalism. The Arab Higher Committee adopted it in 1948, the year Israel was created at the close of the British Mandate.
The Palestine Liberation Organization adopted the current arrangement in 1964, which gave Palestinians everywhere a single flag to use, and the Palestinian National Authority took it up later. It is the flag of the State of Palestine, and it flies at international forums alongside other national flags.
The four colors
The three stripes and the triangle are the Pan-Arab colors, and each is tied to a period of Arab history. Black is the Abbasid Empire, and is also read as grief for lost sovereignty. White is the Umayyad caliphate. Green is the Fatimid caliphate, with religious associations. The red triangle is the Hashemites, the dynasty that led the Arab Revolt, and it also stands for the blood of martyrs.
Jordan, Sudan and Libya use the same palette for the same reason: all of them trace back to the Revolt's flag. Jordan's is the closest match to Palestine's, and the differences come down to the arrangement of the bands and what is added on top.
Where the flag appears
Inside the Palestinian territories the flag is everywhere, and it functions the same way among the diaspora. Political factions have produced their own adaptations, adding elements or inscriptions that carry a particular line.
Outside Palestinian communities the flag has become the standard emblem of solidarity campaigns, and it turns up at demonstrations well beyond the region. It also runs through Palestinian painting, literature and music, usually in work about endurance.
References
[1] "Palestine Liberation Organization Document Sources" (https://www.palestine-un.org)
[2] Smith, Whitney. "Flags Through the Ages and Across the World." McGraw Hill, 1975.
[3] "United Nations Records on Palestine." (https://un.org)