What does particle & wave nature of a substance mean?

I think you're asking about "Wave-Particle Duality". Wave–Particle Duality is the concept that every "elementary particle" or "uantic entity" exhibits the properties of not only particles, but also waves. Is "light" a particle with mass and substance? Or, is it just a wave traveling through space? Most scientists say light is BOTH a particle and a wave! Light, that is, visible, infrared, and ultraviolet light, is usually described as though it is a wave. We talk about light being a form of electromagnetic radiation, which travels in the form of waves and has a range of wavelengths and frequencies. Blue light has a smaller wavelength; red light has a longer wavelength. So we know that light has properties of waves. But Scientists have also found various evidence to suggest that light was not really a wave, but more like a particle. To solve the problem, famous scientists like Einstein, Hertz and de Broglie had to put their heads together and come up with a better solution for how to think about light. Their contributions led to the current scientific theory of Wave-Particle Duality. In 1905, Albert Einstein suggested that we should sometimes think of light as a particle, instead of a wave. He said that if we imagine light to exist in little packets of energy, then all of our observations make a lot more sense. Think of that beam of light as though it were a stream of tiny energy packets. Each packet has a mass of zero, so it doesn't weigh anything. Each packet contains a certain amount of energy, which it can transfer to the electrons when it strikes the metal. Einstein called these packets light quanta, but now we call them photons. read less

The behaviors of the electron does not allow for it to be observable as a particle and as a wave. The two sided nature of the electron is known as the Wave-Particle Duality: The property of particles behaving as waves and the property of waves behaving as particles as well as waves. Although the duality is not very effective in large matter. The wave characteristic of the electron implicates many of the electron's particle behaviors. read less

It simply means whether the atoms and molecules of substance are behaving like particle or a wave. Suppose if the substance behaves as a particle It will have following phenomenon like reflection, refraction, total internal reflection. But suppose substance is behaving like a wave then it will have interference,etc. Light has both nature. It behaves as a particle and wave both, which is known as dual nature of light. read less