The light is a symbol of remembrance. It springs from the head of the First Spirit, the spirit of the past. Scrooge attempts to put it out by means of a cap that the Spirit also carries, but the light continues to flood out from under it. He does not succeed, therefore, but merely falls into an exhausted sleep. This is symbolic of how all his memories, and his softer, younger self have been re-awakened in him by the visit of the Spirit; he can never forget, he can never go back to being the old hard crusty man that he was at the beginning of the story.
When the Spirit of Christmas Past appears before him, Scrooge desires "to see the Spirit in his cap"; that is, to cover the light of knowledge from memories that it spreads through the room.
"What!" exclaimed the Ghost, "would you so soon put out, with worldly hands, the light I give? Is it not enough that you are one of those whose passions made this cap, and force me through whole trains of years to wear it low upon my brow?"
However, he is unable to do this because the Spirit of the Past is too strong with its long muscular arms. Memory's light persists. When Scrooge disclaims any intention of "bonneting" the Spirit at any time in his life, the Spirit refutes this claim by saying that it has come for Scrooge's "reclamation." It orders Scrooge to stand up and walk with him. When the Spirit moves toward the window, Scrooge pleads with it that the weather and the hour are not appropriate for travel, but the Spirit tells Scrooge to lay his hand upon its heart. As Scrooge does so, they are swept away to the time when he was a boy. Memories begin to flood Scrooge's mind and he "reclaims" the memory of his young self as a lonely boy. This recall of his own misery reminds him that a boy was singing a Christmas Carol at his door and he ignored him. Now, however, he sheds a tear, wipes his eyes and tells the Spirit, "I should like to have given him something; that's all."
Thus, the knowledge provided by memory of one's own loneliness and misery extends its light into the heart of Scrooge and he realizes that he should have relieved another boy's same misery with a kindness to him.
When the ghost of Christmas Past comes to Scrooge, he tries to show Scrooge scenes from his childhood. He is trying to make Scrooge see that the things of the past have affected the man Scrooge has become. The ghost has a flame of light above his head and a cap that he carries to put the light out. Scrooge soon realizes that he can't put the light out.
Scrooge is shown things from his lonely childhood. He is made to face the events of his past, that have affected his future. They are painful memories for Scrooge and when he sees them, he feels the loneliness and sadness that he experienced as a young boy. When he sees himself as a young boy at the school, he remembers that his father sent him away and had no contact with him. When he sees his sister, Fan, he is reminded at how much he loved her. She was the only person he had. She was the one who came and got him from school to take him home. When he has to relive her death, it breaks his heart all over again. All of the events of the past that Scrooge is shown, make Scrooge remember all of the hurt he once felt as a young boy. He doesn't want to have to relive any of it, so he wants to extinguish the light, so he can make the memories stop. He tries to place the cap over the flame, but realizes he can't make the light go out.
The light represents the events of the past. They are always there and no matter how hard we try to make them go away, there is nothing we can do. The memories are always there. It is up to us whether we embrace them and learn from them, or try to bury them and have them revisit us at a later date, but they will always come back.
In a Christmas Carol, Scrooge tries to extinguish the light by placing the cap over his head. He could not succeed because the light is a symbol of truth. The truth cannot be extinguished, therefore, neither could the light.