Most lenses will create a certain amount of corner shading or vignetting - especially clearly seen in skies or similar backgrounds.
Canon has measured how much fallingoff there is for each Canon lens and defined a profile for each. The Peripheral Illumination Correction will correct for this unevenness.
The setting process is quite easy. Enter the menu of the camera and find the utility in the bottom of the first red tab. You can enable/disable the function here and see whether the data for the attached lens is available.
With the camera connected to the computer you run the programme EOS Utility (part of the programme package delivered with the Canon camera). Select "Camera Settings / Remote Shooting" and select "Peripheral Ilumin. Correct" from the menu. Now you can define the Canon lenses you would like to use the Peripheral Illumination Correction with. Many lenses are already chosen for you - you can remove some lenses you are not likely ever to use. Do you have a 1.4 Canon Extender or a 2.0 Canon Extender - these are also available for the most obvious lenses.
The camera will either correct for the vignetting immediately in the creation of the JPEG image or will store the information in the RAW file for later use in the DPP (Digital Photo Professional - Canon's RAW conversion programme).
Have a look at this very illustrative video by David Newton.
