The light sensitive neurons of the retina (120 million rods and 6 million cones) pass their electrical signals through several intermediate layers to ganglion cells, which extend about 1.5 million cell fibers (the optic nerve) into the brain for further processing. Passing through the LGN in mid-brain, the signals end up in the visual cortex at the back where their processing eventually lead to our perception of visual objects and events.
Now, the rods and cones fire when light falls on them, they are simple photoreceptors. Ganglions, on the other hand, receive inputs from a large number of photoreceptors, so we'd like to know their receptive field. The receptive field of a ganglion is the region of the retina that effects its firing when stimulated. Kuffler (1953) showed that cat ganglion cells have a receptive field with a "center surround" pattern:
Note that these cells will respond strongly to a patch of light with the right size and location, but unlike rods and cones, they will not respond strongly to a uniformly bright surface because the excitatory (+) and the inhibitory (-) areas will approximately cancel out.
Hubel and Wiesel (1959) went further and recorded from the neurons of the cat visual cortex to identify their receptive fields. Their attempts at trying to elicit response from cortical neurons with spots of light were unsuccessful in the beginning. A couple of hours into the experiment they accidentally discovered a neuron that "went off like a machine gun" when inserting a glass slide into the projector. It turned out the neuron liked the straight edge of the slide that was moving on the screen. They discovered cortical neurons (which they called simple cells) respond best not to spots, but to bars of light oriented in a particular direction.
So far we have covered the "what?" part of our story. In the following decades research on computer vision took off at the MIT AI Lab and elsewhere. The engineering approach of trying to build systems that could actually see helped us understand why nature may have "designed" the receptive fields the way it has. For example Marr and Hildreth (1980) argue that the center surround receptive fields can be thought of as convolution with the second derivative of a Gaussian and the simple cells detect the zero-crossings of this convolution which facilitate edge detection.
Engineering approaches may answer the "why" but still leave open the question of how neurons know to connect in this intricate pattern. Embryo development is still not completely understood and while it may be reasonable that the same developmental processes that can build "fingers and toes" may create some functional regions in the brain, it is probably not reasonable to expect instructions for neuron #134267542 to connect to neuron # 49726845. At this point in our story came Olshausen and Field (1996) who showed that if you train a neural network with patches of natural images and bias it to preserve information and promote sparseness, you automagically get receptive fields similar to those of Hubel and Wiesel's simple cells: