Extrinsic elements are those things which come from the outside to influence the story. In Little Women by Louisa May Alcott, several external elements encroach on the story and impose change on the characters and plot.
The first and most obvious one is the Civil War. While there are no real elements of the war in the story (i.e., no battles or politics), it is the war which has taken Mr. March away from his family. He is a chaplain in the war and, when he gets wounded, the girls also lose their mother for a time. Eventually the family is reunited, but their absences do impact the plot.
We hear many words of wisdom from Mrs. March to her girls before she is called away to be from her husband, so we know what she expects of them. After she leaves, we watch her daughters struggle (sometimes successfully and sometimes not) to maintain those standards and precepts. When Mr. March leaves, he, too, sets out the precepts he hopes his daughters will follow while he is gone. When he comes back, we hear him say this about Jo:
"In spite of the curly crop, I don't see the 'son Jo' whom I left a year ago," said Mr. March. "I see a young lady who pins her collar straight, laces her boots neatly, and neither whistles, talks slang, nor lies on the rug as she used to do. Her face is rather thin and pale just now, with watching and anxiety, but I like to look at it, for it has grown gentler, and her voice is lower. She doesn't bounce, but moves quietly, and takes care of a certain little person in a motherly way which delights me. I rather miss my wild girl, but if I get a strong, helpful, tenderhearted woman in her place, I shall feel quite satisfied."
This is significant because we have seen Jo every day during his absence and the changes she makes are, of course, gradual; however, when her father returns he can see the dramatic changes and reminds us of them, as well.
Another extrinsic element in this novel is disease, specifically scarlet fever. Beth does what she is best at: she sacrificially gives of herself to help those who are in need. She is being obedient to both her nature and her parents' precepts, and it is a good thing. Unfortunately, she contracts scarlet fever, which is the direct cause of her untimely death.
One other extrinsic factor in this story is the death, the great inevitability for us all, of the girls' rather crotchety Aunt March, their father's rich sister-in-law. When she dies, she leaves her house to Jo, an act which will change Jo's and her husband's (Professor Bhaer's) lives.
Money, or the lack of it, is a final extrinsic element in this novel. No one in the story gets significantly richer or poorer during the course of the story (though of course Amy does marry someone who is rich); every character simply has to live with his or her financial condition. Though it helps shape each one's actions, it is almost a force beyond their control because of their circumstances.