Inside the eye of the pupil--the aperture that lets light through onto the light-sensitive lining at the back of the eye called the retina. The feline pupil can open about three times as wide as the human pupil, thus letting in as much light as possible at the hunting times of dawn and dusk. The feline eye also has about three times the number of rods (the receptors that are sensitive to light) than we have.
But just letting more light into the eye is not enough--the cat's eye also has a special reflective layer at the back called the tapetum ludium that reflects light not absorbed by the retina when it first enters the eye, and gives it a second chance to be interpreted.
These two adaptations of the feline eye make the cat's night vision 40-50 percent better than ours. They also mean that when the cat's eye is illuminated by a camera flash or by a car headlight at night the eye glows a fluorescent greenish/gold when the light bounces off the reflective area. The principle is put to god use in the reflective studs used on roads to show motorists the way at night (actually sometimes called "cats' eyes")
A third adaptation of the feline eye is it's ability to detect movement--large numbers of special cells are triggered by the movement and, as anyone who has played with a cat by pulling a toy mouse along on a piece of string can testify, the signals produced in the cat's brain trigger a predatory sequence of behavior--it just cannot resist chasing the moving object.
Of course,having eyes that are extremely sensitive to light can cause problems on bright sunny days when the light is very strong. To make sure that the very sensitive system that has been adapted for night vision is not swamped during the day, the cat can shut it's pupil down to a fine vertical slit, at the same time shutting its eyelids--the horizontal and vertical damping ensuring that only a small amount of light enters the eye. Light sensitivity also probably takes precedence over the sharpness of the image on the retina; cats may see a more "fuzzy" image than humans.
The retina is limited in size and by giving more space to rods ( the receptors sensitive to light) rather than to cones (the cells that recognize color) the domestic cat probably sees some blues and greens but not reds in the same way that we do-- they probably look gray. Other species of cat may also see in color it depends on the prey they have been adapted to hnt; if it is highly colored and hunted during the day, they may see the world in much the same hues as we do.
A final protection for the very important feline eye is its third eyelid- a thin flesh membrane that is usually tucked away at the corner of the eye but that can rapidly protect it. It can sometimees be seen when the cat is feeling unwell.
