A light probe is a type of image that contains floating point information for accurate representation of light, and is used to illuminate a 3d scene via radiosity.
Light probes are so named because they are in the form of a mirrored ball, so the image is a 360 degree panorama from the point of view of the probe. It may be kind of hard to make any sense of a light probe image because of the form it takes. It is a true 32 bit image (the RGB images you normally see aren't true 32 bit, they're 8 bits per channel, 3 channels, 8*3=24).
As a result it can show more information than you are capable of seeing at once, for the purpose of extrapolating information to the radiosity for flawless compositing. If the light probe is not a true HDRI image then artifacts occur, which ruin compositing, and no one likes that. As to the mirrored ball format it uses, to visualize it just look at the center as the area directly in front of you, and the edges of the ball as the area directly behind you.
Paul Debevec has made huge advances in the field of realistic radiosity lighting, HDRI, and real timefacial reflectance lighting, and anyone wanting to learn more about it from the source should check out his website at http://www.debevec.org/.