Nagisa is quite probably my all-time favorite female lead in any anime. Ushio is adorable as well...really I just love the whole Okazaki/Furukawa family.
She did but she didn't.

Yay Key...basically, they set it up where getting one of these 'lights' granted you a wish. Tomoya got one from his dad when he reconciled their relationship, though I guess he didn't realize it at the time. When Ushio died, he wished desperately just to have a happy family. Which he got by, more or less, going back in time and Nagisa being cured.
There's more to it...but that's the jist of it. Hope that makes some sense.