The moral of A Christmas Carol has everything to do with the transformation of the main character, Ebenezer Scrooge. He begins the story as a miserly, closed-hearted man. Through the events of the novel, he is transformed into a man whose heart is open to the pain and struggle (and love) of others, a man who has become someone who will participate in the world around him, rather than withdraw from it.
Dickens wrote his novels during a time when the society around him was changing rapidly. The working world, especially the world of a city like London, was becoming more mechanized, more factory-based, and it seemed to Dickens that the needs and good of the common man were slipping through the cracks. In all of his works, he appealed to his readers to empathize with those who are without -- the poor, the destitute and the orphaned.
The moral can be found in Scrooge's transformation at the end of Chapter Four. Scrooge says:
'Good Spirit,' he pursued, as down upon the ground he fell before it: 'Your nature intercedes for me and pities me. Assure me that I yet may change these shadows you have shown me by an altered life!'
'I will honour Christmas in my heart, and try to keep it all the year. I will live in the Past, the Present, and the Future. The Spirits of all Three shall strive within me. I will not shut out the lessons that they teach.'
His appeal shows the moral, which is that it is never too late to begin to act in a loving and caring way towards one's fellow man in, as Dickens saw it, the necessary Christian spirit of love, forgiveness and generosity.
To me basically the moral of the story was that everyone can change. Sometimes we withdraw our selves from the world and become a lot more colder than we were in the past.
Everyone needs someone to care about them. Change is always there, sometimes there are lessons to be learned.