"Sarah will talk to me about someone and I don't know who she's talking about, but if she talks to my mother, the two of them will know exactly - and across several generations, too"

Prince Andrew is most likely referring to the truth that Sarah and his mom have a shared history and knowledge of people that he does not. Sarah might be talking about someone from their past, and his mother will have the ability to complete the information. This shared knowledge and understanding of individuals and events is most likely something that has been given through generations, and is something that Prince Andrew does not have access to. He is likely expressing his adoration for the connection that Sarah and his mom have, and the fact that they can communicate and understand each other without having to describe the details. This quote is a testimony to the power of shared history and the value of giving understanding and understanding from one generation to the next.