Symbolism in a story is usually an object or thing that represents a meaning that is different than what it actually means. 
In Of Mice and Men
The dream that George and Lennie talk about in the story is a symbol of how people dreamed of having a happy and free life. They want to believe that there is a possibility that they can live their lives and do things their way and not have to do everything the same way that everyone else is forced to do.
Another symbol would be Lennie's dog. Throughout his life, Lennie struggled to control his strength and he often got into trouble because of it. When he was little, his Aunt Clara used to bring him mice and he always ended up crushing their heads so she eventually stopped bringing them. Later in his life, he killed his puppy and then Curley's wife. His strength got him killed since he couldn't control it.