In 'A Christmas Story', the mom is Mrs. Parker. She is a loving and practical mother. She manages the household with a firm but kind hand, dealing with her husband and two sons. For example, she makes sure Ralphie and his brother have warm clothes and food during the Christmas season. She also has to put up with Ralphie's various antics, like his obsession with getting a Red Ryder BB gun for Christmas.
In the original Christmas story, Mary was the mother. She was a young woman who was chosen by God to give birth to Jesus. According to the story, an angel visited her and told her she would conceive a son by the Holy Spirit.
The original mom from the Christmas story, as seen in the movie, is a typical mom of that era. Melinda Dillon's performance as her is memorable. She is constantly looking after her family. Whether it's making sure Ralphie is warm enough in the cold winter or trying to keep the peace when things get a bit rowdy in the house. She has a nurturing side, but also shows a bit of firmness when necessary, like when Ralphie gets into some minor trouble.