Most early reports of her shooting listed her as dead. My belief is that this is because people hear "shot in the head" and immediately translate that into "dead". Many surgeons would, as well.
However, according to the BBC, Giffords' surgeon, Peter Rhee, was "a former military doctor who served in Afghanistan" and her neurosurgeon, Michael Lemole, "removed half of her skull to give the [brain] tissue room. The bone is being preserved at a cold temperature and can be reattached when the swelling subsides."
The article does not, however, explain this procedure very well, and so I thought I'd give a little bit of an explanation.
This surgery is known as a decompressive hemicraniectomy. I've published research with people who have had this procedure, blogged about that work, talked about it a TEDxBerkeley last year, and even got picked up by Mind Hacks and Wired for it. Here's what the skull of a person who has had this surgery looks like:
And in 3D:
This surgery is amazing. As I said in the last piece, I worked with a surgeon at San Francisco General Hospital, Geoff Manley.
Dr. Manley has recently published several papers on the clinical benefits of performing a decompressive hemicraniectomy on people who have had some kind of head trauma. To give a little bit of a background, a decompressive hemicraniectomy is a surgical procedure in which the surgeon actually removes a large part of the skull (see the picture at the right) after someone has had head trauma that has caused the pressure inside the skull to increase. This can happen in a few ways, but basically, because the head is an enclosed system, if the brain swells arteries can get pressed closed. This can cut off the blood supply to different brain areas. The swelling can also cause the brain to press down onto the brainstem which can lead to coma or death.
There is a scale that is used to describe someone's neurological state after a head injury. This is known as the Glasgow Coma Scale (GCS), which is a numerical scale ranging from 3 to 15, which 3 being nearly dead. A person who shows up with a GSC of 3 can even be viewed as a lost cause, with very little chance of survival. Points are assigned based upon observations of the eyes, movement, and verbalization by the patient. A 3 would mean the patient does not open their eyes to any stimulation, has no movements, even in response to pain, and makes no sounds.
One of the patients we worked with in my study had a GSC of 6 in the field, which dropped to a 3 by the time he got to the hospital. That subject
...underwent an emergency decompressive hemicraniectomy and removal of the subdural hematoma because of his rapid neurological deterioration. At the time of EEG testing, he was doing remarkably well and had no evidence of any residual neurological or behavioral deficits.
Subject 1 sustained a gunshot wound to the left frontal lobe anterior to premotor and motor cortices. His Glasgow coma scale (GCS) was 14 on admission. The patient was taken to the operating room for debridement of the gunshot wound, and a decompressive hemicraniectomy was performed to prevent further neurological deterioration from increasing ICP [intracranial pressure] from the initial penetrating brain injury. At the time of EEG testing, his memory, attention, and motor function were normal and he did not have any frontal release signs. Of note, the patient is currently back to school.
Now, of course I'm not a medical doctor, have no details about Congresswoman Giffords' medical state, or anything like that. But hearing that her neurosurgeon performed a decompressive hemicraniectomy gives me hope that she may well recover from this attack.
Anyway, I hope this serves as a way of some explanation of what her surgery was, and why it was performed.
EDIT: I've written an even simpler explanation of this over at Quora:
Basically, the gunshot caused tissue damage of the actual brain tissue. This leads to swelling. Of course, the head is an enclosed space, so the brain tissues can only swell up onto the skull causing compression and threatening to cut off blood supply or down, through the opening at the base of the skull (foramen magnum) causing a herniation (in this case, and "uncal herniation"). This swelling down onto the brainstem stem compresses the tissues there, damaging the neurons. The brainstem neuronal structures are responsible for basic functions required for life such as respiration and maintenance of consciousness. Damaging these tissues leads to rapid degeneration of status, coma, and then death.
EDIT #2: Looks like CNN's Dr. Gupta agrees with me.
Voytek B, Secundo L, Bidet-Caulet A, Scabini D, Stiver SI, Gean AD, Manley GT, & Knight RT (2010). Hemicraniectomy: a new model for human electrophysiology with high spatio-temporal resolution. Journal of Cognitive Neuroscience, 22 (11), 2491-502 PMID: 19925193