The worn-out carpet, along with other visible signs of wear and tear in their apartment, suggests that the Youngers are struggling financially. They are likely unable to afford to replace or repair the carpet, so they have placed furniture over the worn areas to cover them up.
This arrangement of furniture also symbolizes the family's efforts to maintain a sense of pride and dignity despite their difficult circumstances. By trying to hide the imperfections of their home, the Youngers are demonstrating their resilience and determination to make the best of their situation.