One of the most interesting property of waves is that when two waves pass through each other, their effects are added together. This is called interference.

Imagine a light source being blocked by a sheet of metal with two slits in it. A few meters away there is a screen. For a given point along the screen, there are two light waves hitting the screen (one through each hole). These two light waves travel different distances to reach the screen, so they interfere with each other, creating an interference pattern.

It turns out that if you carry out a similar experiment using a particle beam instead of a light source, you record a similar interference pattern. This means that all particles have wave properties. For example, here's a real interference pattern caused by an electrons scattering off gold foil:

It is a very strange concept that what we think of as solid matter particles are, in reality, wave-like because matter particles have wavelengths, and can interfere with each other.