Blindsight was discovered Larry Weiskrantz and Alan Cowey at Oxford while examining a patient suffering from cortical blindness in the left visual field.
For details on blindsight please read the other writeups in this node.
The explanation for blindsight remains controversial. The main reason is that one of the popular explanations for blindsight, involving connections to the superior colliculus (as explained in the above writeup), leads to the reasonable conclusion that most people with visual cortex damage will exhibit blindsight -- it so happens that many patients do not show any signs of blindsight, and many of those who do have blindsight only have it for part of their visual field. (Scharli, Harman, & Hogben, 1999; Wessinger, Fendrich, & Gazzaniga, 1997).
One of the other explanations is that within the damaged area of the visual cortex there may be small areas of undamaged tissue, not large enough for a conscious experience but nevertheless enough for blindsight (Fendrich, Wessinger, & Gazzaniga, 1992).
A further explanation is that after damage to the primary visual cortex, other cortical areas get enough visual stimulus from the thalamus to produce blindsight (Moore, Rodman, & Gross, 1998).
As we can see from this confusion, the inference is that unfortunately researchers do not yet know much about visual consciousness. The dominant hypothesis is that consciousness is distributed over several cortical areas (Zeki, 1998).
If we move back to the leading argument -- which says that alternate pathways in the brain supply visual information to the superior colliculus, but we are not conscious of this -- then one can pose the question of why is it that we are only concious of the visual information reaching the primary visual cortex?
Vilayanur Ramachandran gives the example of driving a car whilst having a deep conversation with a passenger in the car -- providing nothing out of the ordinary happens on the roads your driving experience becomes completely subconscious and, in a way, is similar to blindsight. You can perform the highly sophisticated task of traffic negotiation subconscously; but amusingly, you cannot devote your full conscous attention to driving and leave your conversation on "autopilot".
References:
Biological Psychology, James Kalat, pp. 178
Vilayanur Ramachandran's second lecture for the BBC Radio 4 "Reith 2003" lecture series:
http://www.bbc.co.uk/radio4/reith2003/lecture2.shtml