This is a key moment in the text. We have already been presented to the mother, who becomes obsessed with her supposed lack of money to the point when even the house is filled with strange voices saying "There must be more money! There must be more money!" The children, growing up in this environment, are obviously impacted by this insatiable hunger for more money, which leads to the conversation that Paul has with his mother:
"Oh!" said Paul vaguely. "I thought when Uncle Oscar said filthy lucker, it meant money."
"Filthy lucre does mean money," said the mother. "But it's lucre, not luck."
"Oh!" said the boy. "Then what is luck, mother?"
"It's what causes you to have money. If you're lucky you have money. That's why it is better to be born lucky than rich. If you're rich, you may lose your money. But if you're lucy, you will always get more money."
It is important to note that the word "lucky" plays a very importnat role in the story. The mother's assertion that luck determines whether or not a person has money indicates her single-minded focus on wealth and its acquisition and gives Paul the mistaken impression that to be lucky is to be wealthy, whereas, obviously, there are lots of different ways in which you can be lucky. It is this conversation that places Paul on the path to self-destruction as he inspires himself to be ever luckier to gain more money for his mother. The ending of the story clearly shows how destructive this view is, as the pursuit of luck and money leads to Paul's death, ironically giving the mother what she wants, but taking away one of her most precious possessions.