A light field is a represetation of light, a way to describe the light (image) in a scene. A light field camera can record the "entire" light information in a scene (all light rays arriving at the lens - the intensity and direction of each light ray). A light field display can recreate this information into an image - which is a "true" 3D image similar to the real world.
Lightfield cameras are very useful as they record more information than a regular camera. You can change the focus and aperture in a lightfield image after you take it, for example. 3D lightfield cameras are especially useful to recreate useful 3D content for VR/AR applications. There are some lightfield cameras already on the market, for example from Lytro, one of the pioneering companies in this field. Lytro offers professional cinema cameras, consumer cameras and special 3D camera systems.
Lightfield displays are beginning to emerge, although these displays are not available commercially yet. The basic concept is to take a lightfield image and then display it on a regular display with an array of microlens array on top. The microlens help recreate the original image to many viewpoints.