Scrooge, before his encounters with Jacob Marley and the three ghosts of Christmas, is concerned only with that which is productive, efficient, and lucrative.  The single-minded pursuit of these make him a powerful man.  A child, in contrast, represents much that is contrary to Scrooge's former values; children are not generally very productive, efficient, lucrative or powerful.  In fact, they are dependent, often ignorant, and powerless, and these things the old Scrooge would have detested and avoided at all costs.

The fact that Scrooge asks the child what day it is shows how greatly he has been changed by his strange night.  In asking, he is validating the knowledge of a child, giving the child authority.   This is why it is so important that a child is the one to tell him that it is Christmas day; the knowledge and authority of Christmas is placed in the hands of a child, a person who by society's standards (and the old Scrooge's) may be dependent and powerless, but who by Scrooge's new understanding of human value (love, charity, community), is a person of great importance.

After his partner Marley appears to Scrooge, telling him that he must walk the earth in payment for his sins, and Scrooge is taken on torturous journeys through the past, present, and future Christmases with the three ghosts, Ebenezer vows to the Ghost of Christmas Future that he will honor Christmas each year and strive to keep its spirit in his heart throughout the year, holding his hands in prayer as the spirit disappears.  Then, in Stave Five Scrooge awakes in his own bed, elated that he will be allowed to make amends. Thus renewed in spirit, Scrooge declares,

"I am as light as a feather, I am as happy as an angel, I am merry as a schoolboy...."

and he "whoops" and "hallos" in giddiness.  Not knowing how long he has spent with the spirits, Scrooge cries out that he does not know what day of the month it is, but he does not care, for he would like to "be a baby," meaning he wishes to just enjoy life without concerns and, in a way, begin his life again.  Therefore, it is fitting and significant that Scrooge asks a child what day it is,

"Today!" replied the boy. "Why, CHRISTMAS DAY."

Reborn with the joie de vivre of a youth himself, he sends the boy to fetch the "prize Turkey" at the Poulterer's, vicariously taking delight in the boy's running "off like a shot."  As he himself walks along the streets, Scrooge has a joyous expression upon his face; he greets people and acts generously toward the old gentleman to whom he had heretofore been cruel, he visits Fred and celebrates Christmas with his family.  On the next day, he raises the salary of Bob Cratchit. Much like a boy, "His own heart laughed: and that was quite enough for him."