"Old Fezziwig" is Mr. Fezziwig, the kindly, jovial warehouse owner to whom Ebenezer Scrooge was apprenticed as a young man and who appears in stave 2, "The First of Three Spirits," in Charles Dickens's A Christmas Carol.
The Ghost of Christmas Past takes Scrooge back to his past in London, to a part of town in which Mr. Fezziwig's warehouse is located. Scrooge is elated to see Mr. Fezziwig again, "an old gentleman in a Welsh wig"—not a wig at all but a kind of knitted woolen cap made to cover the head and the back of the neck, which gave it the look of a wig—sitting behind a high desk where Mr. Fezziwig works on his papers and books and from which vantage point he observes and supervises the activities in the warehouse.
It's Christmas Eve, and at the hour of seven, Mr. Fezziwig lays down his pen, rubs his hands together, laughs all over himself, and calls out to a young Ebenezer Scrooge to close up the business for the day. While young Ebenezer and his fellow apprentices close up the widow shutters, Fezziwig calls out for them to clear some space in the warehouse to make room for Fezziwig's Christmas Eve ball, a yearly event attended by all of the warehouse workers, Mr. Fezziwig's wife, three daughters, and their extended household, the baker, the milkman, and even a shy, hungry lad from a business across the street who's lured into the warehouse by the table laden with meat, pies, and beer.
Scrooge and the narrator repeatedly refer to Mr. Fezziwig as "Old Fezziwig," but "old" seems more like a term of endearment than a physical description. There's no indication that Mr. Fezziwig is elderly or in any way decrepit. Quite the contrary is demonstrated by his dancing ability and the boundless energy he exhibits throughout the evening's festivities, which show him to be, if not particularly young in age, then certainly "young at heart."
The party ends at eleven, and Mr. and Mrs. Fezziwig station themselves on either side of the door to wish a "Merry Christmas" and give a hearty handshake to everyone who attended the party as they pass through the warehouse door and out into the London night.
The older Ebenezer Scrooge was so caught up in the infectious happiness of the moment that he entirely forgets about the Ghost of Christmas Past, who Scrooge finds looking intently at him when all the guests have departed.
The Ghost of Christmas Past plays the devil's advocate for a moment and cynically remarks that is was a small matter for Mr. Fezziwig "to make these silly folks so full of gratitude." Scrooge is somewhat taken aback at the remark. Then Scrooge and the spirit listen to the young Ebenezer and his fellow apprentice, Dick Wilkins, express their heartfelt praise for Mr. Fezziwig, after which the spirit continues in the same vein, "He has spent but a few pounds of your mortal money: three or four perhaps. Is that so much that he deserves this praise?”
Scrooge passionately defends his former employer, who he clearly loves, respects, and admires.
“It isn’t that, Spirit. He has the power to render us happy or unhappy; to make our service light or burdensome; a pleasure or a toil. ... The happiness he gives, is quite as great as if it cost a fortune.”
As he speaks, Scrooge realizes that he's forgotten the lessons that Mr. Fezziwig taught him about the way to treat employees, family, and friends. Scrooge scorns his family—particularly his nephew, Fred—and has no friends. Scrooge makes the work of his own employee, Bob Cratchit, not happy, light, or pleasurable but unhappy, burdensome, and toilsome.
In a moment of regret, recalling the example of Mr. Fezziwig, Scrooge tells the spirit, "I should like to be able to say a word or two to my clerk just now."