Symbolism is when an object, action or character is used in a text to stand for both itself literally and usually a more abstract concept or principle. If you think about it, we live in a world of symbols where everyday objects that we are bombarded with such as logos and signs are used as symbols of larger ideas. For example, if you see a picture of a cross, this is a widely recognised symbol of Christianity. In the same way, a dove is recognised as being a symbol of peace.
In texts, you might like to think about how objects, characters and actions can be used to communicate quite complex and detailed symbols. For example, if we look at a famous scene from A Tale of Two Cities when a wine cask is broken in the streets of Paris, this event is used as a very powerful symbol for the desperate nature of the peasants' hunger and poverty. The way in which they are described as desperately lapping up the wine and the efforts that they go through to extract the last drop from this sudden bounty emphasise the hunger for food. However, there is also implicit in this symbol a hunger for freedom and equality.
In addition, the way in which the wine is compared to blood suggests the symbolic way in which this scene is used to foreshadow the bloodthirsty and violent ways in which the peasants will seize those freedoms when they have the chance through the revolution. This effectively foreshadows the terrifying scene at the grindstone in Book the Third.