Basically all you really need to know is that Tohru is just about as unstoppable a force of Shy Cute as Sora is a force of Exuberant Cute, and also that Tohru got semi-adopted by a bunch of people who happen to turn into the twelve Chinese zodiac animals when hugged by a member of the opposite sex (no, they don't really explain why).

It should still be funny, I hope, though you'll get more of the in-jokes if you know more about the Fruits Basket characters and story line...