Aunt Alexandra plays a vital role in this story, as do all of Lee's characters. Atticus is an uncoventional person and parent. He believes in understanding the viewpoints of others and in remaining true to your own sense of individuality. However, this viewpoint is not championed by society, which always wants citizens to fall into certain "roles." Everything moves smoothly if you accept your role and act accordingly - that way, everyone else knows how to treat you and what to think about you.
Aunt Alexandra adheres to these rules in society. She provides Scout with a contrasting manner of behavior, so that Scout can compare Alexandra and Atticus and come to her own decision about how to act and what rules to follow. For example, Atticus is happy to let Scout wear what she wants. Alexandra believes she should dress like a young lady. It will be up to Scout to decide which belief will best suit her.
The other important point of this character is that Alexandra is dynamic. Scout puts Alexandra into the role of bossy and opinionated, and thinks that Alexandra is just plain unfair. However, as Scout has been learning, you should never judge anyone before walking in his shoes. At the tea party, Scout learns that she has underestimated her aunt, who is intelligent and compassionate.