I think this case is well-known thoughtout the US, not just in Florida, but of course folks in other countries need some background.
Without any research or fact-checking, here's what I know off the top of my head:
Terri Schiavo has been in a vegeatative state for years and years, and would not have been able to survive without medical intervention ~ the feeding tube, certainly, and perhaps some other technology as well.
Her husband is on one side, wanting her to be taken off life-support so she can "die with dignity." Her parents (and siblings?) want to keep her alive.
She does have her eyes open and can move her head, neck and facial muscles, and observers differ over whether this indicates any consciousness on her part. Disinterested observers with scientific/medical credentials seem to agree that she is not conscious or in any normal sense "alive." On the other hand, she is not, strictly sp[eaking, "brain dead" either, and the parents take the facial animation as a sign that their daughter is alive and wants to stay alive.
Courts have recently ruled for the husband. I think that he has not divorced her, despite having formed a relationship with another woman, for the specific purpoe of maintaining his position as Terri's closest "next-of-kin." The parents are outraged that an "adulterer" has a stronger legal claim on their daughter's life than they do, and have called for the support that now seems to be coming from well-organized fundamentalists.
Incidentally, I read a recent news report that Terri Schaivo had a history of eating disorders prior to her collapse into the coma or vegetative state or whatever it is. I'm not sure whether bulimia might have been a contributing factor to her current state.