The game "Monopoly" existed and was patented several times prior to its official publication. The earliest patents were by Elizabeth Magie in 1904 and 1924. There were a fair number of regional variations and many of the early boards were homemade, although there were small print runs of official boards as well. These early versions went under a variety of names including Landlord, Finance, and Prosperity and in England Brer Fox an' Brer Rabbit. They gained particular popularity amongst Quakers and the Georgist school of economists. So the early players tended to be either religious or college students. And the board tended to take on local flavor. Magie's 1924 board for example included Chicago streets like The Loop and Lakeshore Drive.

Eventually a man named Eugene Raiford learned the game in Atlantic City. He took his Atlantic City board with him to Philadelphia where Charles Darrow encountered the game. He published his own version, using those Atlantic City names. He also got a patent for his version of the game. His patent and design was sold to Parker Brothers a year later, and became the basis of their version, Atlantic City names and all. Parker Beothers also went out and bought out all the other patents and copyrights they could find at the time. So that's how the Atlantic City version became "canonical" despite being a late development.

Early pieces were generally things found in a household, so buttons, beans, and thimbles were common types of playing pieces. When Charles Darrow published his version, he had found a supplier of charms for ladies' charm bracelets and included them in his game so that buyers wouldn't have to provide their own pieces. Parker Brothers stuck as closely to the Darrow patent as possible, so as to defend their claim to own a game that had been in existence for 30 years before Darrow's patent was issued. That included sticking mostly to the pieces that Darrow included in his game, although they did swap out some for pieces that they had molds for because they were in use in other games, namely the "battleship" and the "cannon."

I'm not aware of any meaning attached by Darrow or Parker Brothers to the pieces.