Also known as the V1 area and the striate cortex, this area of the cerebral cortex is the most important brain area for overall visual processing. It is the first area connecting the visual input system (fed in from the eyes) to the cortex proper, and seems to be responsible for a great deal of low- to mid-complexity visual processing. Also, it takes up a comparatively huge amount of spatial area on the cortical surface, about 5% in humans, 15% in macaques, and so forth -- generally, percentages negatively correlate with total cortical surface area. The precise limits of V1 function in the phenomenon of sight, as well as all of its interrelations with other brain areas, are currently being researched by thousands of scientists, though some of the elementary function seems to be well established.
When light hits the eyes, each retina passes a signal down its optic nerve to the lateral geniculate nucleus, which is located roughly in the dead center of the head between the tips of one's ears. The LGN's purpose is essentially to convert the input from the optic nerves, which are ipselateral (i.e. wired either all on the right side or all on the left side) to the bilateral (i.e. wired to both sides) inputs used by V1. From the LGN, axonal fibers reticulate out and synapse at the primary visual cortex, which is located at the most posterior part of the occipital lobe -- more or less at the furthest back part of the brain. If this seems unclear, especially the bit about the LGN, keep reading and hopefully it will get a little better.
V1 itself, much like the rest of the cerebral cortex, is divided into "columns" of interconnected neurons. Each column, as determined by single electrode measurement tests, seems to be preferentially sensitive to a single kind of visual stimulus, and most neurons in the column have that same sensitivity regardless of depth. Virtually all of them are at least somewhat orientationally sensitive, meaning that they fire best when their visual input is a border in some certain orientation -- that is, some prefer vertical lines, others horizontal, others lines at a 29° angle and so forth. Roughly 30% of them are also directionally sensitive, meaning that they fire when an edge in their input is moving in a certain direction. Other cells have preference for certain ranges of color, certain degrees of luminance, and probably other features notable in vision.
These columns are arranged into stripes on the cortex, hence the "striate" in "striate cortex". Tested in one direction, a stripe has columns which respond to some certain orientation, sometimes called iso-orientation stripes. Tested in the perpendicular direction, orientation preference through all 180 degrees, but ocular preference tends to be either for the left eye, the right eye, or both eyes. In other words, from the bilateral output of the LGN, left- and right-eye inputs for the same areas of the retinas synapse next to each other on V1, in a relatively orderly fashion.
Along the centers of these optical dominance stripes, that is, between the areas most strongly activated by only left or right eye input, the perpendicular iso-orientation stripes encounter what are known as "pinwheels" or "singularities". Viewed in terms of orientation, a singularity looks something like a whirlpool, with orientation being roughly radial at some distance from the center, and tending toward more circumferential as one moves toward it. As it happens, these singularities are roughly one millimeter away from each other (in primates and cats, as tested), meaning that there is an underlying large-scale periodic nature to the cortical surface.
Using these singularities as reference centers, groups of columns can be collated into what are known as macrocolumns or hypercolumns. In every macrocolumn there is sensitivity for stimulus from both eyes, in all orientations, all directions of movement, all colors, and so forth. Each of these structures corresponds fairly well with a certain small area of the retina; these are individual phosphenes, the low-level "pixels" that make up the visual field. Macrocolumns are isotropically (i.e. the same in all directions) connected within themselves, which is to say that stimulation of some part of one either inhibits or excites most of the rest of it. More interestingly, each is also anisotropically connected to neighboring macrocolumns -- a column sensitive to a particular stimulus synapses to columns with the same sensitivity located in other macrocolumns. It is this anisotropy which makes the columns individually sensitive to a given directional line, which may only be perceived as such by consideration of more than one column.
Layout of the macrocolumns is not as simple as one might think, given the one-to-one correspondence to the retina. Light receptors are densest on the fovea, an area of the retina usually located directly behind the lens. Hence, more of the LGN output is composed of foveal input than of input from the rest of the retinal area, so more of the visual cortex must be dedicated to it. To understand the mapping, think of the retina in polar coordinates, with the fovea roughly at r = 0, and receptor density decreasing as r increases. Because we can see (ignoring the blind spot) in all directions, this mapping is swept through all θ = 0 to 2π radians of rotation. This must be mapped onto an array of equally-sized macrocolumns, which don't have the luxury of changing their density to meet the circumstances. To do so, r is made logarithmic, i.e. x = log(r) along the x axis, while θ is stretched out, say y = θ onto the y-axis -- a curve on the retina thus may look like a line or spiral of activation on V1, a straight line corresponds to a parabola, etc. An upshot of this mapping is that a stimulus on the outside part of the retina not only stimulates fewer receptors, but is also processed significantly less than one closer in.
V1 interconnectivity with other brain structures is quite complex as well, and by no means completely understood. For one, it can give feedback to the LGN, perhaps in order to regulate the amount of signal sent from it. It also connects to other parts of the visual system: the supplementary eye fields (possibly responsible for visual attention and gaze shifting), the frontal, parietal, and medial temporal lobes (analysis of motion, i.e. the M-system or "where" system), and the inferior temporal lobes (object identification, i.e. the P-system or "what" system). Also, it receives and processes feedback from these areas.
Developmentally, the system seems to be a self-organizing system which is not hard-wired at birth except for the retina-LGN-V1 pathways. Experiments show that visual stimulus must be presented while the area still has high neural plasticity; if kept in the dark past a certain age, no amount of visual stimulation will enable the organization required for sight. Also, certain features may be controlled for in an experiment, and the visual cortex will grow to accept only those. For instance, in one experiment a cat was raised which was only able to see in vertical lines -- horizontally moving stimuli were entirely lost on it.