Pronouns are where you replace proper nouns with more generalized terms such as he, she, we, they, us, them, etc. For example, instead of saying "Susan, Jeffrey and Sam went to the movies last night," you would replace the proper nouns (the official names) with a suitable and grammatically correct pronoun. In that sentence, the pronoun you need is "they." So, the sentence would read, "They went to the movies last night." Pronouns help to simplify speech a bit, and not make it so repetitive; it would get tedious and difficult to repeatedly say, over and over again, "Susan, Jeffrey and Sam," if you were going to keep talking about all of the things that they did after the movies. It's much easier to say "they," and the audience knows who "they" is referring to, because you've already named them.
In "The Gift of the Magi," there are really only two main characters--Jim and Della. To keep saying their names over and over again is redundant. So, O. Henry replaces their names with "he" and "she." If you look at the paragraph that begins with "Della finished her cry," you see the pronoun "she" and "her" all over the place. Those two pronouns, she and her, are referring to Della. One other pronoun you see is "him." That refers to Jim, who Della is contemplating in that part of the story.
I hope that those thoughts help to clarify what pronouns are for you, and to find a couple in the story; good luck!