Electrons are easy

Sure. So, imagine a rectangular pool of water. You have a little weight on one end of the pool bobbing up and down producing waves. Then you put a wall halfway down the pool with two gaps in the wall. The waves from the wave-generator hit the gaps and go through. At the back wall of the pool you can measure the wave height. What you see is that at some points there are big waves, and at other point no waves at all. What's happening is that the waves coming through each gap travel different distances. If the wave from one gap is at a trough when the wave from the other gap is at a peak, they interfere with each-other and the water doesn't move much. If, instead, the distance is right so that both waves are at a trough or both waves are at a peak, the wave height is doubled at that point.

If the weight bobbing up and down is very regular, the pattern stays very regular. The places on the back wall with no waves are always in the same spot, and the places with big waves are in the same spot.

Now, do a similar experiment but instead of using water, you use light. To keep the waves all the same wavelength / frequency, you need a laser. So that laser shines forward and hits a barrier with two small slits in it. When the laser hits a wall after that you get the same pattern of bright spots and dark spots. Light is acting like a wave and the light waves are interfering with each-other in the way you'd expect.

But, what if you turn the laser way down. You can reach a point where instead of getting a continuous pattern on the back wall of the experiment, you only get an occasional "blip". What's happening there is that the intensity of the laser is so low that you get a single photon being emitted, passing through the slits and hitting the back wall.

So, this basically shows that light is acting like a particle. It is emitted from the laser, passes the slits, and hits at one single, specific point on the back wall. So, this shows that light is both a particle in some ways (individual light "packets" can be emitted and strike one specific spot on the back wall), and it's a wave, because the light passing through the two slits interferes and produces a strong/weak pattern on the back wall.

But, the truly mind-blowing part of the experiment is what happens if you record the positions of each hit on the back wall when the laser is tuned way down and only emitting one photon at a time. If you record the location of the hits (or say, use something like photographic film that you expose over multiple days while you run the experiment), what you see is that there are points where you get many single-photon hits on the back wall, and points where you don't get any single-photon hits on the back wall. And, the points where you don't get any hits are exactly the points where you get dead zones from the wave interference when you run the laser at full intensity. Even though you're only allowing one photon to go through at once, it's still acting as if it's going through both slits in some way.

The obvious question at that point is "Which slit is it actually going through?" So they measured that, and as soon as they could determine which slit the photon went through, the interference pattern disappeared. Instead it looked exactly how it would look if you blocked the other slit. But, when they stopped measuring which slit the photon went through, the interference pattern comes back.

This revealed a few fundamental things in quantum mechanics:

1. Everything is both a particle and a wave. That applies to things we mostly think of as particles like protons and electrons, but also to things that mostly act like waves like electromagnetic radiation (light, gamma-rays, x-rays, radio waves, etc.)
2. Measuring fundamentally changes the result. It's not possible to observe passively. This isn't just a vague statement though. There's an equation that says that the uncertainty in position multiplied by the uncertainty in momentum is always bigger than a certain value which is related to the Planck Constant. It's a tiny, tiny value so it doesn't much affect human-scale things, but massively influences things at a sub-atomic scale.
3. For many quantum phenomena, something can be in an indeterminate state and interact with the world in some ways until something forces the quantum state to collapse. Instead of going through either of the two slits, there's a probability distribution about its position, which doesn't collapse until it interacts with the back wall of the system, which forces the wave function to collapse and results in a single spot being produced on the back wall.

It’s probably worth finding a good educational video about.

Basically, the particles really are waves. Even though they’re particles.