The kufiyyah is worn by all male Arabs. If the movies are accurate, the Hebrews at the time of Moses and Jesus wore it too. It’s a way to keep the sun off your head. Lawrence of Arabia wore one during his campaign. Chayim Weizmann wore one as a symbol of friendship when meeting with Emir Faysal, who accepted the Balfour Declaration.
BUT, the black-and-white checkered kufiyyah has become a symbol of Palestinian terror because it was what Yassir Arafat always wore. I would not be caught wearing one of those. It sends a bad message.
I think the "checkered" pattern is worn after a muslim has completed the "Hajj".