When using the Canon in one of the auto-exposure modes, this knob lets you tweak the exposure to your liking.
For example, if you are shooting a subject against a predominantly black or dark background, when the camera auto-exposes for the entire frame your subject may be overexposed. Likewise a subject against a bright background may be underexposed. You can use the AE shift knob to compensate for that, basically it moves the "average brightness" reference point up or down.
This only works in auto-exposure modes, of course. If you shoot in full manual mode (as the good lord intended), you can turn the AE shift knob all day and it will do absolutely nothing.
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