From CNN:
Schiavo suffered brain damage in 1990 when she collapsed from heart failure. She recovered from the heart attack, but oxygen was cut off to her brain. leaving her in what doctors call a "persistent vegetative state." She is responsive to stimuli, doctors have said, but has no significant brain function and cannot feed herself.
It's a tough situation really. Her parents obviously don't want to let her go, and think there's still a glimmer of hope that she may recover somewhere down the road, and thus their fight to keep her alive. They say she still "responds" to them, so they're praying for a miracle.

As for her being stuck in the vegetative state, yeah - that's truly horrible, and if she really did tell her husband long ago that she never wanted to be like that, then her wishes should be followed, and she should be allowed to pass away peacefully. She probably should be granted that regardless.
Very sad story...