Her daughter had already spent her allowance that week. Limits give others important information about you to help them know what they can or cannot expect from you. They are about you. Not about criticizing someone else's behavior or about trying to make them act in a certain way. Children need you to set limits so that they can recognize and respect other people's limits.
Limits provide a sense of security.
When children don't know your limits they feel lost in an abyss. They feel confused and sometimes literally bounce around trying to find some. Limits make children feel like we care about them. Children who are raised without limits often feel abandoned. Children need limits to learn how to deal with conflict.