Charles Chesnutt wrote "The Wife of his Youth" to make a social statement. When he wrote this story, it was a difficult time for African-Americans. Slavery had been abolished and African-Americans were trying to integrate into mainstream society--a difficult task. Because many African-Americans were mixed race, the lighter complexioned people had more upward mobility because they looked closer to white people.
In this story, the main character, Mr. Ryder, is fair-skinned and a respected member of the blue vein society. He, like the other members, believes that they should marry and socialize with light-skinned people in order to advance more easily in society. When Liza, his first wife, comes back into his life, Mr. Ryder is conflicted because she is very dark, uneducated, and representative of a lower class of African-Americans--the very class he is trying to escape. By accepting her at the end and acknowledging her as his wife, Mr. Ryder shows that while they may be anxious to move up in the world, they must not forget their past or their heritage. That is the purpose Chesnutt had in mind when writing this story--remembering one's past.