Use the word represent when something stands in for something else — whether it's your congressman representing your interests in Washington or the thimble that represents you as it makes its way around the Monopoly board.
We live in a democracy in which we elect a few people to represent the wishes and desires of the rest of us. Their job is literally to "re-present" the voters' demands in Congress. That's why we call them our "representatives." In the world of art, however, to represent something can mean to express its essence by means of something different. For example a ball of string can represent, or symbolize, a cat.