Single slit diffraction
The most simple picture about diffraction comes from using the Fraunhofer case (both source and detection screen at infinity) and Kirchhoff's approximate formula. Then the diffraction pattern seen at the screen turns out to be given by the Fourier transform of the openings, i.e., the electric field is proportional to this Fourier transform.
The physical picture behind this is that any point of the opening is the source of a wave, and at the infinitely far away screen you can approximate the spherical wave by a plane wave (Fraunhofer diffraction).
You find the math in great detail at the Wikipedia link in GeneralOJB's posting.