We've all heard about it. Symbolism, when combined with an already-strong story can make that story into a classic. It can take a great plot with great characters and give it meaning. Conversely, the same is true if you were to take it away from a story, because part of the magic would go with it. (Imagine Les Miserables without symbolism, and suddenly it turns into a really drawn-out action story)
So, using symbols in your writing is important. But how do you go about doing it?
In each of the important scenes of the book Stephen King discovered that there was blood. Blood itself can be very symbolic, so he decided to play with it. He did, and the story is the result. By making the symbolism powerful he turned what in my opinion would have been a typical horror story into a story that has resonance with the reader. It will be remembered, when others that were similar but lacked that symbolic nature fall by the wayside.
One of the best examples of using symbolism in movies that I can think of is the 1999 flick Varsity Blues. (Please note, I didn't say it was the best movie ever, but I like it because it's so easy to see how they used symbolism).
The story is about a high school football team in a small town in Texas. A coach, played by Jon Voight, rules the town with an iron fist. A small band of the best players must decide through the course of the movie if they are going to save their own possible futures in football or sacrifice them to end the long chain of abuses and get rid of the coach.
In all these examples, however, story comes first. Symbolism can effectively add to your story, but you've got to make the story work in the first place. Characters have to be strong. The plot has to feel organic. If you're able to do these things, then sit down and read through it, and see if anything stands out to you. Maybe something you can emphasize more. If not, oh well, you've still got a great story. But if so, play with it and see what you can come up with.