In the story, the Swallow's love for the Reed keeps him from accompanying the other birds to Egypt. The Swallow courts the Reed all summer, despite the warnings he receives from the other birds about how "ridiculous" his attachment to her is, that she has "no money" as well as "far too many relations" (all of the other reeds down at the river).
The other birds turn the Swallow against the Reed, and then they depart for Egypt; the Swallow began to think of the Reed as a "coquette" because she "is always flirting with the wind." The Swallow wants to travel and see the world, and he decides that the Reed is too domestic for that life. When the Reed refuses to go away with the Swallow, he gets angry and flies away, and this is when he first sees the statue of the Happy Prince.
Of course, the Swallow fails to join his friends in Egypt once the Prince begins to ask the bird to stay and help him. Despite the cold, the Swallow says, he feels quite warm after helping one of the poor villagers who benefits from the Prince's generosity. The Swallow eventually decides never to leave him.
Perhaps, then, the Reed represents something other than this kind of generosity—when the Swallow gets to help people and make a difference in the lives of others, he is willing to sacrifice even his own life, something he was not willing to do before for the Reed. Maybe, then, the Reed represents more egotistical desires, and may imply that we must abandon these before we can really serve our fellows and make a difference in the world. In addition, the Reed refuses to leave her home, just as the Prince's home is of paramount importance to him, and the Swallow did not understand this when until he met the Happy Prince. Perhaps this is meant to illustrate, through the Swallow's behavior, the value and importance of home.