When light passes through a small hole (such as the aperture iris in your camera's lens), it spreads out. This diffraction visibly reduces image sharpness. The smaller the aperture, the greater the effect. Diffraction occurs to some degree at small apertures with all lenses, but is more visible on photos taken with digital cameras than in film cameras, because the pixels on the digital camera's sensor are more sensitive than film is to the softening effect of diffraction.
The exact aperture at which the softening caused by diffraction becomes visible depends on several variables, including sensor and pixel size. Generally speaking, the smaller the sensor, and the smaller the pixels on the sensor, the sooner you'll notice the effect of diffraction as you stop down. This is one reason that compact cameras often have a minimum aperture of around f8; the diffraction at smaller apertures may cause an unacceptable degree of softening. On my full-frame EOS 5D Mark II, softening caused by diffraction becomes visible at around f22 when I use my EF 17–40 mm lens so photos taken at f22 are actually softer than photos taken at f11, despite the increase in depth-of-field.