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Quite often when looking at reviews of lenses I will see mentioned that setting an aperture of F11 will give the best results with this lens or that lens.

Can anyone explain why this is?

well most lenses don't work there best at there extreme's wether this is aperture or zoom so for instance a 70-300 zoom will be it's weakest in terms or sharpness particularly at 300mm and wide open(it's largest apeture) stopping down or reduceing the apeture is a good way of increasing the sharpness of the lense because you increae the tollerances of the lense there is a bunch of physics behind that that i don't understand enough to explain but basically by stopping down and incresing the DOF and decreasing the sensitivity of the lense you are able to (with the approriate shutter speed and/or stable platform) get a sharper photo

Also, diffraction. On DX sized sensor, it theoretically kicks in at around f/16 (one stop down from f/11).