In case you're curious, it looks like someone uploaded the scene to youtube. It doesn't quite have the same impact when you don't know the characters but I'm sure you can get the general idea.
A reviewer once mentioned that in Fruits Basket, good parents are about as common as penguins in the Sahara. Lets just say that the best ones of the bunch tend to just be corpses and it goes sort of downhill from there. The entire story is full of people feeling like outcasts for one reason or another with all sorts of various emotional wounds. But, as the saving goes for some couples, the bumps in his head fills the holes in hers. All the characters end up leaning on one another and what once seemed broken, all ends up fitting together by the end.
The explanation for the title tells you a lot about it.
The title of the series is taken from a children's game, Fruits Basket, in which the participants sit in a circle, and the leader of the game names each person after a type of fruit; when the name of a child's fruit is called, that child gets up and has to find a new seat. When the protagonist, Tohru Honda first plays this game in kindergarten, she is assigned "Onigiri" (rice ball), by her cruel classmates, but she does not mind because she thinks onigiri are delicious. Once the game is finished, and all of the children but Tohru are called, Tohru realizes that onigiri are not a type of fruit at all, and she realizes that she does not belong.
I just finished downloading the manga a little bit ago and I'll probably try to read it at some point. I'm not a huge fan of manga in general, but the anime only covers part of the story as I just found out. I figured I should go back and read it from the start and see what I missed.