What Are Genealogies?

Just a question, what is God saying to us throught these genealogies that are scattered in so many places throughout the Bible? When I look at Ezra 2, I wonder if I am not seeing something like a survivors list. In Matthew and Luke the genealogies are important because they link Jesus with the royal house of David for one thing. ( An aside: Why wasn't the question of descent from David the first question put to Sabbatai Zevi and other false messiahs?) But these explanations aren't enough. What is God saying through these lists?