For a long time there was some debate as to whether light was a wave or a particle. For example, the reflection of light can be explained just as easily using particles as waves. However diffraction is a phenomenon that only waves exhibit and forms the basis of the experiment.
The experiment is easy to do, but difficult to understand. It consists of setting up a light source on one side, facing a barrier (such as a piece of cardboard) that has two slits in it to permit some light to pass through to a distant wall on the other side. If both slits are open, a distinct pattern of bright and dark bands is observed on the distant wall. This is known as an "interference pattern". If one slit is covered, a different pattern is seen on the distant wall. The fact light undergoes diffraction means that it has wave-like behaviour.
Other experiments, such as the photoelectric effect can only be explained assuming light consists of particles. So along with the photoelectric effect, this experiment demonstrates the wave-particle duality of light.
The experiment can also be done with particles such as electrons. When many (perhaps 1000) they are accelerated at two slits, an interference pattern emerges. This shows the wave-like nature of matter. Wave-particle duality was proposed in 1924 by Louis De Broglie, as he considered if light can behave as particles, should the reverse be true. The wavelength of a particle can be found as: