A dangerous medical condition caused by overexposure to UVB light, which burns out the cornea (the protective covering) of your eye. Basically, it's an optical sunburn. Snowblindness occurs most often in arctic climates or at high altitudes, where you get the killer combo of freezing temperatures, thin atmosphere and reflected sunlight from snow and ice.
Though it typically takes an hour or two for a really serious case to develop, a mild case can occur with only a few minutes of unprotected exposure, even on a cloudy, overcast day. Especially on a cloudy day, since the haze simply serves to reflect even more light into your vulnerable eyeballs.
Note that snowblindess is not the same as getting "dazzled" by a bright light (i.e. after-image). After-image is caused by damage to the retina (the sensors inside your eye), not the cornea. The other thing that sets snowblindness apart is that the symptom of blindness usually seems only secondary to the intense, excruciating pain that comes along with it.
The pain is typically described by those who have experienced it as "like having sand thrown directly into your eyes. Continuously. For 12 hours." Other symptoms include: tearing, redness, headache, swelling around the eyes and acute light-sensitivity (obviously). Actual loss of vision only occurs in the most severe cases. Usually, partial sight is still possible, albeit very blurry and red-hued, as if seeing the world through rose-tinted glasses (but without all the cheeriness and glee).
Most dangerous of all, however, is that-- just like a sunburn--- you don't notice the pain right away. It usually takes 8-10 hours for the symptoms to really set it. About the only immediate symptom is a growing inability to distinguish colors. If your gear is starting to look a different color than it did when you started out, you may be in serious trouble.
Luckily, the damage is only temporary. Even bad cases will eventually subside in a day or two. In the meantime, there's not much you can do besides applying a cold compress, some pain-killing eyedrops, and maybe an ophthalmic antibiotic solution (like Ocumycin) to prevent infection. These will only help to decrease the pain and irritation, though. The only way to get your vision back is simply to wait for your corneas to repair themselves.
Snowblindness most often effects high-altitude mountain climbers. Prevention is as simple as wearing UV-shielding eye goggles, but having your goggles fog up in difficult terrain can force a rather tough decision. Often, even veteran climbers will remove their goggles if they become too clouded or scratched, opting for the temporary advantage of vision while knowing full well that they'll be in a world of hurt by the time they get to safety.
sources: MedicinePlanet (http://www.travelhealth.com), MountEverest.Net (http://www.mounteverest.net), Snowboard Britain (http://www.snowboardbritain.com)