Elizabeth Bennet is arguably one of Jane Austen's most beloved characters. I personally believe this is due, in part, to her characteristic honesty and ability to make what some might describe as "outspoken" a quality of grace and admiration.
Elizabeth Bennet has high standards both for herself and others. Because of this, she is often critical, but not necessarily mean nor rude. Actually, she's often quite funny. Her quick wit and ironic (or dry) sense of humor were not exactly socially acceptable for women in her society, which only shows her boldness and confidence to be herself even when it isn't necessarily "fashionable" to do so.
Throughout the novel, we see Elizabeth's struggle between saying and acting out exactly what is on her mind or practicing the self-control that is expected of her. We're proud when she accomplishes either, because she manages to make every decision through a perspective of learned intelligence combined with common sense. Because she herself is authentic, she is attracted to others who have a strong sense of self.
Her stubbornness too is a loveable quality, because this means Elizabeth Bennet is not perfect. The majority of her problems stem from her equal parts "pride" and "prejudice." Really, the foundation of the entire novel is summed up in this one character, who grows from beginning to end in finding a balance between these qualities.
Elizabeth is the second of five sisters in the Bennet family. She is a young woman "not yet one and twenty" who is at a marriageable age but refuses to accept the socially expected notion that a marriage has to be formed to solidify family names, finances, and land. Lizzie Bennet is a pioneer of her time because she is not socially worried about marrying or not, and because her ultimate aim is to be truly happy.
Her character also reflects a difference among her peers: She is outspoken, opinionated, and does not care whether who or what rank the person is to whom she has to tell her opinions to.
She holds a very special place in her heart for her sister, Jane, and understands the weaknesses and limitations of the rest of her family members. This makes her a true supporter of her family, despite of their defect.
One of the most important characteristics of Elizabeth is that her father adores her. That is significant because to hold the esteem of a man surrounded by bickering women all day, and whose own wife is a pain, means that Elizabeth has earned that respect for being clear in thought and action. This is probably what also set her aside to win Darcy's heart.
Another point to add is to consider how Elizabeth represents the title of the novel. Where and why is she prideful and what are her prejudices? How do those qualities and notions affect her interactions with all of the various characters in the novel?
She is obviously quick to judge and holds her prejudices against others for quite awhile. Darcy makes a poor first impression, and Elizabeth takes a significant amount of time to come to a truer understanding and appreciation of him. She doesn't even see the light when he first proposes -- it is only after he defends himself against her false charges in regards to Wickham, that she realizes her erroneous prejudices. Until then, she believed Wickham's lies because she wanted to believe them. The lies seemed to fit her assumptions about Darcy.
While her prejudices keep her from Darcy, it is her pride that ultimately unites her with him. Elizabeth shows a significant moment of personal pride in her final show-down with Lady Catherine. Elizabeth is not going to let someone of Lady Catherine's stature bully her into a decision. She stands up for herself, her family and her position in society. While she doesn't have a title, she is still proud of her own person, and this strength and pride proves to Darcy that Elizabeth does care for him and gives him the courage to try a second proposal.