The story of 'Great Expectations' follows a young boy named Pip who lives with his sister and her husband. After helping an escaped convict, he unexpectedly receives a fortune from a mysterious benefactor, leading him to London where he pursues his love for the beautiful but cold Estella. The narrative unfolds through Pip's trials, including the revelation of his benefactor's true identity and his eventual return to humble beginnings, highlighting themes of wealth, love, and social class.