There are a lot of powerful tools in literature and writing, and when you’re discussing abstract themes, symbolism is absolutely one of them. If you want the dictionary definition, symbolism is using imagery, comparison and characterization to represent non-concrete themes. While that sums it up nicely however, symbolism goes a little farther than that.
In some cases, symbolism is also used to represent specific elements of a story. It also happens in real-life as well. Here in America, we have state birds, state flowers, and in my home state of Arizona, our capital city uses a particular mythical symbol: that of the phoenix. New Zealand does the same thing with the delightful kiwi bird, adopting ‘kiwi’ as an name for its native and local citizens. If you’re looking for examples of this on the page, look no farther than Game of Thrones, with the dire wolves of House Stark, or the mocking jay from Hunger Games that Katniss Everdeen is both represented by and represents herself. There are thousands of other examples, both real and figurative.
Using symbolism isn’t particularly complicated. Recurrent imagery allows you to lace a piece with a theme or meaning, but it also means that whenever you use that particular image, readers are liable to pick up on that. You’ve probably heard the joke about the teacher describing how the author meant a character was sad and depressed because the curtains in the room were blue. That’s symbolism at work.
Another way symbolism works is through comparison, and frequently in figurative language. Often anger is symbolized by blades, knives or steel. Characters with ‘steely’ gazes are angry, upset or ready to destroy an obstacle. Those with sharp voices are similarly in unpleasant and unhappy moods.
When using symbolism, you need to be aware that regardless of what you use, it is very much influenced by connotations. Doves a symbol of peace, however they are very similar and related to the maligned pigeons who might end up as symbols of city overcrowding and filth.