What does "The Gift of the Magi" teach us about true love?

From Della's point of view, her appearance is of less importance to her than her love for her husband, Jim. She is willing to sacrifice what she assumes to be her best feature, her beautiful long hair, in order to buy a present that will express her love for him. When Jim comes home from work, he is astonished by her appearance. She must look entirely different with all that hair replaced by tight little curls held in place by hairpins. But his love for her is of much greater importance than her appearance. He is only astonished because he has sold his watch in order to raise enough money to buy her a Christmas present: a set of combs for her vanished hair.
“Don't make any mistake, Dell,” he said, “about me. I don't think there's anything in the way of a haircut or a shave or a shampoo that could make me like my girl any less."
Neither of them has really lost anything as long as they still have each other. As Shakespeare writes in his Sonnet 116:
Let me not to the marriage of true minds
Admit impediments. Love is not love


Which alters when it alteration finds,
Or bends with the remover to remove:
O no; it is an ever-fixed mark,
That looks on tempests, and is never shaken;
It is the star to every wandering bark,
Whose worth's unknown, although his height be taken....
O. Henry is saying that true love is not, and cannot be, based on mere appearance. Della loses her beautiful hair but gains something more important: the assurance that Jim truly loves her. And Jim loses his valued watch but gains something more important too: the proof of Della's love for him. No doubt both of these young people realize that they have been attaching too much importance to material things.
A popular Irish folk song of O. Henry's time, based on a poem by Thomas Moore, expresses the same thought as Shakespeare's sonnet. The first lines of the song are the best known:
Believe me, if all those endearing young charms,
Which I gaze on so fondly to-day,
Were to change by to-morrow and fleet in my arms,
Like fairy gifts fading away,
Thou wouldst still be adored, as this moment thou art,
Let thy loveliness fade as it will....
https://www.owleyes.org/text/gift-magi/read/the-gift-of-the-magi