In May 1801, Thomas Young did his famous double-slit experiment. Some light was fired at a sheet with two very thin slits with the intent of understanding whether light was made of particles or waves. The idea was that if light was made of particles, we'd see a different pattern at the other end of the sheet than if it was made of waves. This experiment eventually helped establish wave-particle duality -- the observation that particles like photons and electrons sometimes behave like particles, and at other times like waves.
When I learned about this experiment in physics class in school, I spent a lot of time thinking about what electrons really were. Were they particles? Or waves? Or did the conditions of the experiment cause them to transform from particles to waves? I pictured a tiny sphere hurtling towards the slits, then suddenly exploding and transforming itself into a wave.
It took me many years to grasp the real answer - electrons are neither particles nor waves. Particles and waves are models of behaviour of macroscopic entities, but they don't apply very well to the world of subatomic particles. An electron is a thing that seems to sometimes behave like a macroscopic particle, and sometimes like a macroscopic wave. In reality it's neither -- the true nature of an electron is something that the human brain, living in the macroscopic world, is incapable of visualizing.