Charles Dickens was observant enough to appreciate how childhood experiences can shape the individual. In A Christmas Carol, the presentation of Scrooge's childhood and youth in stave 2 serves a variety of purposes, all of which are meant to show how Scrooge came to be the misanthropic miser of stave 1.
Firstly, the flashbacks to Scrooge's childhood and youth show that he was once an innocent boy. He was not born greedy or callous. Once, he was able to appreciate kindness, companionship, and imagination. The same man who covets money and shuns holiday invitations from his nephew was once close to his little sister and riveted enough by fantastical fiction to imagine Ali Baba standing outside his schoolhouse window. Dickens is emphasizing that people are born good and only become corrupted due to the influence of the adult world, which emphasizes the wrong things. It is only through recapturing the inner child that one can be saved, and this is where the importance of memory comes into play.
Stave 2 emphasizes the importance of memories not only as a sort of "guide" to an individual's present behavior but also as a possible route to reclaim innocence. When Scrooge is taken to his old school, he proclaims he could walk through it with a blindfold. This suggests more than his familiarity with the grounds: it foreshadows his spiritual rebirth in the final stave, in which he is able to once again attain a state of childlike glee and openness.
By observing his past behavior from the vantage point of old age and loneliness, Scrooge is able to see what truly made him happy in life (his family, his friends, merrymaking) and what a waste of time it has been to pursue money over those other things. Therefore, memory becomes a way of reassessing the past and reshaping the present and future.