It’s complicated, and requires even more spoilers from bloodlines. So, Spoilers from that book.
What happened was that this Noble title for one planet passed with no heir, so by default it would be handed down to Leia. This planet, however, was known for it’s really, really long ceremonies, and it was a title that was pure formality. Leia, having no interest in it, handed it over to Lady Carise, a Centrist who was also of the “Elder Houses” (As the collection of nobility was called.)
Lady Carise, during the ceremony, looked through her inheritance. It contained a music box (It had a more specific name, but I don’t remember it off the top of my head) with a prerecorded message from Bail Organa himself, who wanted to be absolutely sure that Leia knew who her birth father was when she was old enough.
Lady Carise, wanting to destroy Leia’s attempt at being elected First Senator, and drive a nail into her budding friendship with Casterfo, showed this to him, and Casterfo proceded to show it to the entire Senate.