What is the significance of Della's hair?

The main point of the story "The Gift of the Magi" is the heart behind each of the gifts. Della's hair is one of the things she is most proud of, but in order to demonstrate love for her husband by giving him a good gift, she sacrifices her hair. This represents the true heart behind gift-giving: it is more important to give sacrificially than to give a useful gift. This love that transcends the love of material objects, such as hair and watches, is the mark of a true gift-giver.
By the end of the story, it is revealed that both Della and Jim have given up their most prized possessions to give each other thoughtful gifts. In doing so, they have rendered the actual gifts useless. Della cannot use the combs that Jim bought her, because she has sold her hair, and Jim cannot use the watch chain, because he has sold the watch for Della's combs.
Della's hair is significant because it is the sacrifice she makes for her love of Jim.

Della loves her hair. It is significant because it is her most prized possession. It is lovely, and she has not cut it for so long that it falls below her knees. Living with her husband on a limited income, Della doesn't have many material possessions to treasure, which makes her hair all the more important to her.
Nevertheless, Della is willing to sell her hair in order to raise money to buy an expensive Christmas gift for Jim, her husband. Her love of her hair is important to understand so that the reader can grasp the depth of her sacrifice. That she is willing to give up her most precious possession shows how dearly she loves her husband.
As O'Henry notes at the end of the story, after the ironic mishap with the presents, the mutual love the young couple shows is worth far more than the gifts they buy.

At the most basic level, O. Henry's "The Gift of the Magi" is a story about a woman who sells her hair. This single image dominates the story from beginning to end. It is something that is very easy to visualize, and O. Henry uses it powerfully. First he describes how Della lets down her long hair and almost immediately pins it all back up again. The only purpose for that action is to let the reader appreciate how abundant and how beautiful it is.
So now Della's beautiful hair fell about her, rippling and shining like a cascade of brown waters. It reached below her knee and made itself almost a garment for her.
Then O. Henry follows his young heroine to the parlor of Madame Sofronie, a vulgar businesswoman to whom hair is nothing but merchandise. And after Della returns to her flat with the platinum watch fob for which she made such a tremendous sacrifice, O. Henry describes how she looks without all that beautiful hair. She looks like a shorn lamb.