Notice that "Post" is capitalized. It is a proper noun. It is the name of a newspaper.

It's short for the name of a newspaper, such as The Washington Post. People might also refer to The New York Times and others as simply "the Times." If the local paper ends in "Post" they are probably referring to that. Otherwise, it is likely The Washington Post.

At one time, it was popular for newspapers to give themselves names like "The New York Telegram," "The Toronto Mail," and the "St. Louis Dispatch," "The Charleston Courier." "Telegram," "Dispatch," "Mail," and "Courier" all suggest an urgent message, delivered quickly. Many newspapers were called "[City name] Post," "post" being another word for "mail." "The Washington Post" is one of the most famous newspapers in the United States and is often just called "the Post," just as "The New York Times" is often just called "the Times." (In England, "the Times" means "the London Times!")