When we say that an electron has both a particle and a wave nature, it means that its behavior can be described using concepts from both particle and wave theories. This may seem a bit counterintuitive, but let me explain it in simpler terms.
Let's start with the particle nature of an electron. In the context of particles, an electron can be thought of as a tiny, discrete entity with mass and charge. It behaves like a tiny "billiard ball" in some ways. For example, it can be localized at a particular position, and it can interact with other particles by colliding with them, just like billiard balls do.
On the other hand, the wave nature of an electron refers to its ability to exhibit wave-like characteristics. Waves are more spread out and can interfere with each other, creating patterns of peaks and troughs. Electrons can also exhibit similar behavior. This is particularly evident in experiments like the famous double-slit experiment, where electrons are sent through a barrier with two narrow slits. Instead of behaving like particles and hitting the screen behind the slits in two distinct spots, they create an interference pattern that is typical of waves.
So, in a nutshell, the wave-particle duality of an electron means that it can behave like a discrete particle in some situations and like a spread-out wave in others. It's not that the electron is switching between being a particle and a wave at different times, but rather that its behavior is described by mathematical models that incorporate both particle-like and wave-like properties.
This phenomenon is not unique to electrons. Other fundamental particles, such as photons (particles of light), also exhibit this duality. It's a fundamental aspect of quantum mechanics, the branch of physics that describes the behavior of particles at the atomic and subatomic level.
Keep in mind that this explanation is a simplification, and the actual nature of electrons is more complex and best understood through mathematical formalism. Nonetheless, I hope this helps you grasp the concept of electron wave-particle duality in a layperson's terms.