A ray of light falling on a smooth surface bounces to the previous medium at the glancing angle, which is termed as the reflection of light. If light passes from one medium to the next, its speed changes and takes a new direction at the boundary unless the ray hits normally to the boundary surface, which is called refraction of light. A ray of light passing through a very narrow hole, of the size of the wavelength of light, will spread and a pattern of bright and dark regions are obtained at a fairly large distance (relative to the size of the hole) behind the hole, which is termed as the diffraction of light. If a ray of light hits two narrow holes, very close to each other, the pattern obtained is really interesting-the width of the bright and dark regions are the same and the phenomenon is called the INTERFERENCE of light. When a ray of light passes through some medium like calcite crystal (even through air, water, etc), the light field (particularly electric field) is confined in a plane, and the phenomenon is called polarization.
Let's go beyond this. Are these phenomena specific to light? What's about other waves? The answer is - all light-like waves - called the transverse waves have these properties. There is another category of waves which shows sound-like behavior - called longitudinal waves also show all the above properties except polarization. Whatever I wrote above was known before the advent of QUANTUM MECHANICS.
What's about the matter-waves? Quantum mechanics treats the moving matter as a wave called a matter wave. Matter waves also show all the above properties as the light waves do !
Consider a beam of monochromatic light (light beam with a single frequency) passing through a closely spaced double slits. What do we observe behind the slits? We observe a nice pattern, called interference fringe, on the screen placed at a fairly large distance behind the slits. What happens here is the interference of light. The two slits act as the secondary sources (Huygens' Principle) called the coherent sources and the waves from there reach the screen in phase or out of phase. If the waves from the slits reach a point on the screen in phase, they will reinforce each other, producing a bright fringe/band. This is called a constructive interference. If the waves from the slits reach a point on the screen out of phase, they cancel each other and a dark fringe/band is produced in there. This is called a destructive interference. But let's think about somewhat weird situation that there is a single photon reaching the slits. Do we still see the interference pattern? If so, how do we explain this? The single photon can go through one or the other slit? What does it then interfere with?
Note: This post is on progress !