The smaller the aperture, the more diffracted incoming light rays. Once the 'circle of confusion' or airy disc exceeds the size of a single pixel on the sensor, you begin to lose lens sharpness. If you imagine two strips of paper, one green, one blue, directly adjacent. Now imagine photons from either side of the adjacent edge passing through a lens which slightly diffracts them.
This results in an obvious merging of the blue/green strips. The more the diffraction the more they merge, the less sharp the images become.
Current APS-C sensors at 18 megapixels have pixels small enough that an aperture of around f/11 is the minimum size before this effect begins. As sensors get more and more dense, the required aperture size gets larger and larger. F/8 is considered a 'normal' aperture and once sensors hit that density then the payoff from increased resolution is significantly less and can impact image quality adversely.
This is why science missions use 2mp CCDs that they know the characteristics of, rather than some 40 megapixel phone sensor.
edit: I've just realised I've typed all this out with the wrong idea. You wanted a simple explanation of diffraction. Imagine a water tank with waves being generated from a source at one end. Put a wall with a narrow hole in the middle of the tank. If the wavelength of the waves is significantly less than the width of the hole, they will for the most part pass through unaltered. As the hole gets smaller, more significant changes to the waves occur. They begin to 'spread out' or 'diffract'. An intuitive explanation is difficult but this is a practical one that makes sense to people.