What were the consequences of Lydia Bennet and George Wickham's relationship in Pride and Prejudice? How did Lydia's obligation to get married contribute to it?

Lydia and Wickham's elopement generates much of the drama in Jane Austen's Pride and Prejudice because their relationship profoundly affects all the principal characters. Lydia's irresponsible behavior — and the fact that she and Wickham do not initially marry — tarnishes the reputation of the other Bennet sisters and potentially damages their prospects of marrying well. As Mr. Collins states following the elopement:

The death of your [Mr. Bennet's] daughter would have been a blessing in comparison of this... They agree with me in apprehending that this false step in one daughter will be injurious to the fortunes of all the others; for who, as Lady Catherine herself condescendingly says, will connect themselves with such a family?

Lydia and Wickham's elopement catalyzes both the Bennet family and Mr. Darcy into action to try and find Lydia, assess the situation, and hopefully orchestrate a marriage to preserve the family's social dignity as much as possible. After Darcy's intervention, Lydia realizes she is indeed "obligated" to marry Wickham, which helps reduce the scandal of their elopement. At the time, young women only left home with a man if they were married, so Lydia's behavior was considered shameful. Formalizing the union minimized the damage to the Bennet family's social standing, and freed Elizabeth, Jane, and the younger sisters from scathing criticism of their association with Lydia. As Elizabeth states before she learns of Wickham and Lydia's marriage: "Our importance, our respectability in the world must be affected by the wild volatility, the assurance and disdain of all restraint which mark Lydia's character."
Interestingly, it is precisely this crisis that draws Darcy and Elizabeth closer together; he singlehandedly goes to London, finds the couple, and compels them to marry, all of which he does out of love for Elizabeth. When she discovers this through Lydia's inadvertent admission and her Aunt Gardiner's letter, Elizabeth realizes Darcy is a selfless man. Thus, a significant consequence of Lydia and Wickham's relationship is that it facilitates the romance between Darcy and Elizabeth.