Is Huygens' principle true or is it a geometrical construction to figure out path of light wave? And how does it explain diffraction? I am asking in reference to physical optics. What I want to know is whether each point does behave like a light source?
Huygens principle (1700s) was a very good at explaining waves and interference for light and water. Using the principle a very good classical mathematical model was developed and explained the 1 or 2 slit diffraction pattern of light. However it did have some problems and to truly explain the diffraction pattern (to the best of our knowledge) the concept of a wave function was developed in the 1900s to explain the photon path. Huygens principle which relies on interference and cancellation could not explain the results of single photon experiments (no interference possible but the pattern eventually emerges) for example.
Actually, all mathematical/physical principles in physics are constructs designed to produce results that accurately predict the results we find through experiments and observations. The "truth" of a physical principle isn't a proper question. Rather, the accuracy of match between its predictions and experimental results, and its consistence with other accepted principles are the main parameters that determine its usefulness and the likelihood that it will be considered an accepted principle.
Huygens' principle is a very useful predictive tool, but it is not absolutely "true". For example, the principle needs to be modified when special or general relativity and quantum mechanics are taken into account.
You also asked how Huygens' principle explains diffraction. There are many, many online answers to that question. Just do a search for Huygens and diffraction.
If a field is subject to a spatiotemporal constraint — such as the wave equation or Maxwell's equations — then what happens at one point at one time influences what happens at another point at a later time. Thus there is a sense in which the first point acts as a source. The challenge is to express the "constraint" in such a way as to make the "sense" explicit.
P.S. (8 February 2020): One "sense" is that the secondary sources, by themselves, give the same wave function in a specified region as the primary sources by themselves. I have tried to demonstrate this from the most elementary possible premises: "Consistent derivation of Kirchhoff's integral theorem and diffraction formula and the Maggi-Rubinowicz transformation using high-school math".
P.S. (15 October 2022): The above link has been updated.