The eye and conventional camera's capture the colour and intensity of light. They need to focus to get a sharp image for a certain distance.
This allows you to reprocess and refocus the light information afterwards.
Storing this extra information takes up about 200 times the space of a classical picture. So the camera's have to sacrifice resolution to keep picture storage size within limits.
Lytro will bring a consumer light field camera to the market next year. An 8GB version costs $400 and stores 350 pictures.
You can refocus some pictures in a demo at their site.