See, at that time, what we now call Italy was a bunch of smaller countries, and Virginia's cousin was part of the group that wanted them to unify. He took one look at his hot, young, close relative and realized the best plan was to get her to cheat on her husband with Napoleon and hope some political pillow talk could turn the tide. Because 19th-century Europe was apparently an alternate-universe Game Of Thrones, complete with a short guy and creepy family relationships.
This is where they used to keep the dragons.
Virginia managed to become the emperor's mistress for over a year, and shortly after it ended he sent troops to unite the peninsula. Historians disagree about how influential she was in making that happen, since various battles and treaties and intrigues were going on at the same time, but she gave herself basically all the credit and was pissed off that everyone else didn't as well.
Even if the countess was a lot less influential with her pudenda than she would like to think, men still found her enjoyable to be around and were willing to pay for the pleasure. She continued to cheat on her husband and made a nice living from it. Eventually, word got around to the unbelievably rich but famously stingy Lord Hertford, and he offered the countess the original indecent proposal: 1 million francs for one night with her.