Diffraction is the bending and spreading of waves as they encounter an obstacle or move through a narrow gap.
A water wave which encounters an obstacle bends around it. The same wave which encounters a small gap in a barrier would spread outwards (into circular waves) from the gap (as opposed to simply going through unchanged).
The degree of diffraction (i.e. spreading of a wave) depends on the ratio of the wavelength of the wave to the size of the opening (in the case of a gap in a barrier):
If the gap-to-wavelength ratio is small (i.e. the gap is much smaller than the wavelength), the wave spreads out much more.
If the gap-to-wavelength ratio is large, there will be much less diffraction. The wave front will move through the gap with minimal spreading around the edges.
However, if the gap is too small, too little of the wave passes through for the diffraction to be easily observable. It is therefore conventional to use a gap which is close to the size of the wavelength in order to observe diffraction.
A stream of particles in classical physics do not experience diffraction when they pass through a gap (i.e. they do not spread out from the opening).