Theme refers to the moral or lesson of a story. You can look at it as the universal message or the lesson learned by one or more characters. In the story, one of the themes is that you can never escape where you came from.
The story is really about a group of African-Americans who try to use their light skin to get ahead in a whites-dominant world. Sadly, there is only so much they can accomplish because they are limited by the prejudice against their race. Mr. Ryder, for example, is described as refined and having good tastes and sophisticated looks. Yet even he is haunted by his past, as he shows the group the wife he married when he was young.
A prime example of how one’s past catches up is the reappearance of Mr. Ryder’s wife; he thought she was dead, but she was not.
And then suppose that accident should bring to his knowledge the fact that the wife of his youth…was alive and seeking him, but that he was absolutely safe from recognition or discovery…
Just as Mr. Ryder acknowledges his past, all of the members of the society will have to acknowledge theirs, and the limitations of where they come from.