Every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the waves.What this means is that when you have a wave, you can view the "edge" of the wave as actually creating a series of circular waves. These waves combine together in most cases to just continue the propagation, but in some cases there are significant observable effects. The wave front can be viewed as the line tangent to all of these circular waves.
These results can be obtained separately from Maxwell's equations, though Huygens' principle (which came first) is a useful model and is ovten convenient for calculations of wave phenomena. It is intriguing that Huygens' work preceded Maxwell's by about two centuries, and yet seemed to anticipate it, without the solid theoretical basis that Maxwell provided. Ampere's law and Faraday's law predict that every point in an electromagnetic wave acts as a source of the continuing wave, which is perfectly in line with Huygens' analysis.
Huygens' Principle & DiffractionAs shown in the picture to the right, when light goes through an aperture (an opening within a barrier) every point of the light wave within the aperture can be viewed as creating a circular wave which propagate outward from the aperture.
The aperture, therefore, is treated as creating a new wave source, which propagates in the form of a circular wavefront. The center of the wavefront has greater intensity, with a fading of intensity as the edges are approached. This explains the diffraction observed, and why the light through an aperture does not create a perfect image of the aperture on a screen. The edges "spread out" based upon this principle.
An example of this principle at work is common to every day life. If someone is in another room and calls toward you, the sound seems to be coming from the doorway (unless you have very thin walls).
Huygens' Principle & Reflection/RefractionThe laws of reflection and refraction can both be derived from Huygens' principle. Click on the image to the right to view an image of Huygens' principle as it applies to refraction. See how points along the wave front are treated as sources along the surface of the refractive medium, at which point the overall wave bends based upon the new medium.
The effect of both reflection and refraction is to change the direction of the independent waves that are emitted by the point sources. The effects of performing the rigorous calculations obtains results that are identical to what is obtained from Newton's geometric optics (such as Snell's law of refraction), which was derived under a particle principle of light. (Although Newton's method is less elegant in its explanation of diffraction.)