The Cratchit family provides the contrast to Scrooge's character.
When Scrooge's nephew comes to the office and invites Scrooge to spend Christmas with him and his wife, Scrooge pronounces the entire idea of the Christmas holiday as being "humbug" and expresses his complete disgust at the celebration.
If I could work my will...every idiot who goes about with 'Merry Christmas' on his lips should be boiled with his own pudding, and buried with a stake of holly through his heart.
As the nephew departs, he extends Christmas greetings to Bob Cratchit, "who, cold as he was, was warmer than Scrooge; for he returned them cordially."
And so the contrasts are established. Scrooge lives by himself, has gruel by his very small fire in his very dreary quarters, while the Cratchit household was small and simple but overflowing with life and love. Scrooge threatens to find a new clerk when Bob affirms that he would like to have the entire Christmas Day off work, but Bob insists that the family drink a toast to "Mr. Scrooge, the Founder of the Feast."
In the end, Scrooge learns the lessons taught by the three visitors, and the Cratchit family - in particular Tiny Tim - present him with immediate and first-hand opportunities to demonstrate that he has learned the lessons of generosity and kindness toward all.