Even though "The Story of an Hour" is a very short story, it is full of symoblism and depth. It has various themes: marriage, love, death, grief, freedom, the repression of women, the confines of marriage, feminism, irony, societal roles, social taboos, marital expectations, and happiness. All of those themes could each be discussed in great detail, and supported within the text.
For symbolism, the greatest example can be found in the very lengthy description of the spring day that Louise views outside of her window. Here we have a very short story, and yet Chopin though spending over a paragraph just on the weather was important enough to include. The weather, the sunshine, birds, and song in the distance, all symbolize Louise's rather unconventional reaction to the news of her husband's death: happiness and freedom. The spring symbolizes a new beginning; the sunshine happiness and freedom, and the distant song the feeling of elation that she will in a minute, fully realize and embrace. That weather scene is highly symbolic of Louise's feelings of being released from the shackles of marriage.
I hope that helped; good luck!