What is the significance of Lydia's elopment with Wickham?
Lydia Bennet's elopement with Wickham is a catalyst that stirs Darcy's heart toward Elizabeth. He takes responsibility for the family's reputation, making sure that Wickham marries Lydia.
When the silly, 16 year old Lydia runs away with Wickham, out of a need for adventure and fun, she does realize what the consequences will be for her family. She actually thinks that she is doing something positive, finding a husband. Her mother is constantly encouraging her daughters to find a suitable husband. However, Lydia is too immature to realize that Wickham is only interested in using her.
Lydia is irresponsible and foolish, she does not care about her sisters or her parents. I think Lydia's motivation for running away with Wickham is a combination of getting away from her boring life and the belief that she will be the first sister to get married.
I think Lydia is stupid and naive, and believes that Wickham is honorable and will marry her. But it is clear, that had Darcy not intervened, Wickham would not have married Lydia. It is only through Darcy's insistence that he marries her and saves the family's reputation.