This is a good and subtle point. In the beginning of the story Scrooge was the embodiment of a cheap curmudgeon. All he cared about was his own wealth and quite frankly himself. For example, he did not want to spend money on coal to heat his office. And when people came to ask for a donation, he would not even think of it.
However, as he experienced what life would be like if he remained on his current trajectory, he came to his senses. It took ghosts (ghost of Christmas past, present, and future) to convince him of his errors.
At the end of the book he changes. He is relived that he is back in the present. He sends a turkey to the Cratchit house and gets gifts for all. He also honors Christmas in the future and most of all he takes care of Tiny Tim.
Based on this, many will say that he was really a good man that needed to have his eyes opened. This might be true, but isn't this for everyone? It might be better to say that he was not better than his words. Who really have ghosts come to change them? Actually three ghosts! You will have to decide.
The statement that Scrooge was even better than his word refers back to the preceding paragraph near the very end of the tale.
“A merry Christmas, Bob!” said Scrooge, with an earnestness that could not be mistaken, as he clapped him on the back. “A merrier Christmas, Bob, my good fellow, than I have given you, for many a year! I’ll raise your salary, and endeavour to assist your struggling family, and we will discuss your affairs this very afternoon, over a Christmas bowl of smoking bishop, Bob! Make up the fires, and buy another coal-scuttle before you dot another i, Bob Cratchit!”
This is Scrooge's "word," or promise. He will give Bob Cratchit a raise and will try to assist Cratchit's family. He will share a bowl of "smoking bishop" with Cratchit that afternoon. He promises to keep a big fire warming the office in the future.
How was Scrooge "better than his word"? Dickens explains in the following paragraph. He did more than he had promised.
He did it all, and infinitely more; and to Tiny Tim, who did NOT die, he was a second father. He became as good a friend, as good a master, and as good a man, as the good old city knew, or any other good old city, town, or borough, in the good old world.
Scrooge became a completely different man. He actually became a friend of the Cratchit family and a second father to Tiny Tim. He was probably responsible for saving the boy's life. Tiny Tim was not discussed in the paragraph in which Scrooge made his other promises to his clerk Bob Cratchit. This love and benevolence towards the little crippled lad was one respect in which Scrooge was definitely "better than his word." In addition, Scrooge became a kindly, philanthropic citizen who was loved and honored by the whole city.
The transformation in Scrooge's character is a little too good to be true. Nevertheless, "A Christmas Carol" has become a classic, and it always has an uplifting effect on the reader, or on the viewer who watches one of the many film versions of the story that are sure to be shown on television at Christmas. Christmas is a time when people feel free to believe in miracles. The story inspires many people to be kinder to others--at least for a little while.