Culture is so important to society because culture is constructed by society. A person can't understand one without the other because one shapes the other, the way people interact with one another and perceive their environment is all a part of culture.
Culture reflects the inner workings of an individual society. For example culture helps to define social situations so people understand how to behave based on that society's cultural norms. For example when an individual goes to a dinner party in the United States, it is customary to bring a host or hostess gift. Culture also defines values, influences personality development and influences career choices. If culture didn't define values, or what is considered right and wrong within the society, then there would be social discord and the society would fail.
Society could not function without cultural norms that assist in governing behavior and values, and culture could not exist without societal influences to create it. They must coexist in order for humans to exist in an organized manner. It is important to note that culture can, and does, change over time as societal norms change, but the members of that society govern that change so the individual members of the society have a level of control over the culture.