The term Centennial indicates a hundred, so it would make sense that the Centennial Celebration is a celebration to commemorate a hundred years. The billboard announcing the event says,
"Welcome to the Centennial Celebration - A Century of Progress - 1835-1935."
Although when Joey and Mary Alice ask Grandma what the celebration is about, she replies that it is "nothin' but an excuse for people to mill around, waste time, and make horses' patooties of themselves," it is clear from the enthusiasm of the citizens that the centennial is a big deal in the sleepy southern Illinois town. The festivities include a parade, a talent show, and various interesting competitions; the men are required to grow beards, and everyone dresses in "historical getup(s)." Although it is never stated explicitly, it is likely that the Centennial Celebration commemorates a hundred years since the first settlers came to the area, establishing the colorful little town where Grandma lives. Grandma says,
"It's the Centennial Celebration...we're all going back to the old days and the old ways for a week" ("Centennial Summer - 1935").