The elopement is a crucial step in the plot development. Keep in mind that as Lydia nad Wickham are eloping, Elizabeth is in the throes of confusion over her attitude towards Darcy. She has regretted her harsh words towards him earlier on in the story, and has spent a wonderful couple of days at his home. She heard glowing reports from his housekeeper and staff about his kindness and good character, and he himself has been all graciousness and civility and warmth to her and her aunt and uncle. So, she is really wondering if her original assessment had been correct. She still battles with holding herself above him though.
When they get the news of the elopement, Elizabeth realizes that she is truly out of the running for Darcy; she is now linked to a huge family scandal. This makes her long to be in Darcy's favor even more. Then, when she discovers, later on, how Darcy actually stepped in and made the situation right, it solidifies her good opinion of him, and her love for him. The elopement brought her down in pride just a bit, and elevated him in her eyes; this all supports the main plotline of Darcy and Elizabeth overcoming their preconceived notions about one another.
This event also allows Darcy to show Elizabeth that he harbors no ill-will towards her, and to show her that he wants to make up for his messing up the situation with Jane and Bingley. It's a chance for him to show her just how good he is, and how wrong she was about her assessment of him.
The elopement was a critical plot element in the storyline, one that turned Darcy and Elizabeth towards one another, revealing to each their own weaknesses and flaws, and providing a chance for them to make amends. I hope that helped; good luck!
In the book "Pride and Prejudice" Lydia's elopement with Mr. Wickham violated everything that was considered decent and appropriate in the society at the time. Victorian society was very oppressive for women but Lydia stepped out of that and into what would later become a bad marriage that would end in divorce. Lydia marries because of romance and lust for Wickham.
Lydia's elopement with Mr. Wickham makes the other sisters appear more chaste and appropriate and also allows Mr. Darcy and the Colonel to further explain their goodness. Lydia's impulsive actions are the opposite of her sister's actions which results in their marrying their intellectual counterparts and making good marriages.