What is the role of the Cratchit family in the novel, A Christmas Carol?
The Cratchit family represent the 'real life' people to whom Scrooge could be kind and charitable, which for Dickens in this novel is a time of giving and generosity more than a Christian religious festival. Bob Cratchit, Scrooge's clerk, is a poor man with a large family to support. In Stave 1, he is underpaid, and overworked, and bears Scrooge only goodwill, especially at Christmas time. Cratchit uncomplainingly bears with Scrooge's meanness, and is contrasted with Scrooge's nephew, Fred, who is relatively well-off, and only wants to invite his Uncle to a family Christmas party, an invitation which Scrooge rebuffs.
In Stave 3, the Ghost of Christmas Present shows Scrooge images of starving children, and mockingly asks Scrooge 'Are there no prisons? Are there no workhouses?' The Ghost then reveals the reality of the Cratchit's poverty at home, and we understand that Scrooge has no idea until now of the Cratchit family struggles, including the care of their crippled son, 'Tiny Tim'. Still, he is dismissive. The Ghost indicates that the crippled child will be dead by next Christmas.
The Cratchits represent both a moral and political crux for Dickens: Christmas is or should be a time of generosity, materially and emotionally, and in the course of the tale, Scrooge undergoes a moral and emotional transformation and ends by treating the Cratchits to a good Chistmas and - we can infer - saving Tiny Tim's life.
The novel was written (in 1843) at a time when the Poor Laws in England were especially severe - condemning even men with (underpaid) jobs to imprisonment for debt. You should look up the writings of T.S.Malthus on 'The Principle of Population' (1798 - but still a work of note 50 years later) - whose treatise on the ratio of food production to consumers considered those unable to support themselves as virtually unfit to live. It was a well-endorsed political notion at the time, and the workhouses were full of men like Cratchit. Dickens reveals the Cratchits as the human face of these innumerable, dismissable 'poor' and gives them an individual, if highly sentimental, human family life.
If you look at Scrooge as the dynamic protagonist in A Christmas Carol, that is, the main or primary character in a work who undergoes change throughout the story, then the character of Bob Cratchitt (and his family) would be a foil. He doesn't fit the definition of an antagonist because he isn't working against Ebeneezer Scrooge, but his presence in the novel serves to highlight Scrooge's cruelty and miserly personality. The two are opposites, and the Cratchitts serve to show an example of the virtuous poor. One of the many themes in A Christmas Carol is that of the perils of wealth vs. the virtuous poor, and it would be impossible to fully explore that without an example of each. The Cratchitt family exemplifies the virtuous poor - never as clearly as during the Christmas feast when Bob Cratchitt toasts to "the founder of the feast." Although the rest of his family, especially his feisty wife, is incredulous that Bob wished to bestow blessings on him, they nevertheless did so. You can't have a Scrooge without contrasting him to a selfless clerk and his son, Tiny Tim.