Symbols can add emotional depth to your story. Chapter 2.23 discusses some game examples in depth; here, we'll look at an example from Crouching Tiger: The sword, in the beginning, has the significance that it once belonged to a master swordsman. Thus, we can assume it is a superior fighting instrument and perhaps is even endowed with a bit of the master's spiritual energy.
By the end of the film, it comes to signify spiritual and ethical purity. Li has been chasing Jen the entire film to get the sword. At one point, he finally gets it from her. When this occurs, she claims she's finally ready to be taught from him only to belie this with another selfish outburst.
Li tells her she doesn't deserve the sword and throws it in the river. The sword at this point means the ethics and spiritual perfection that are the essence of his teachings. It's these teachings that she doesn't deserve.
So, just as the American flag has picked up many emotional associations over time, so does the sword that once belonged to Li's master and that is the focus of much of the plot.