Visual receptive fields
The centre + surround do not cancel completely, as you can see from these mudpuppy recordings. [Image 1] (Werblin and Dowling, 1969, I believe)

One function of a centre-surround set-up is to highlight the contrast at borders.  Most of the useful visual information is from borders/outlines, so this is a method of ignoring redundant information.  The highlighting of contrast borders and ignoring of redundant information explains why the neural image appears different. [Image 2 - right].
Another function of centre-surround fields is to avoid saturation, but this is more complicated to explain. [Image 2 - left] (Diagrams from Cambridge MVST Part IB lecture series by Hugh Matthews)