Vindicated (transitive verb):  confirm, substantiate; to provide justification or defense for : justify

From A Rose For Emily: “So when she got to be thirty and was still single, we were not pleased exactly, but vindicated; even with insanity in the family she wouldn’t have turned down all of her chances if they had really materialized.”

Basically, it means a confirmation. That there can be a chance where she would meet someone to be with the rest of her life.