Wave particle duality. Everything acts like a wave unless it's being observed (interacted with). Just like normal waves can interfere and overlap creating a superposition, the particle's wave can be split into two states that overlap and create a superposition.

When we describe a particle as a wave, it's basically the probability density of where the particle is.

Schrodingher's cat is the go to example of this. There's a 50% chance the cat is alive, 50% chance it's dead. If we describe an alive cat as a wave function, and a dead cat as a wave function, we can add them together and get the wave function of our superposition cat. We can then take this superposition cat, and do all sorts of math on it. Let's say we heat the box up a few degrees. Instead of taking the wave function of an alive cat and heating it up, taking the wave function of a dead cat and heating it up and then adding the two together, we can take our superposition wave function, heat it up and we get the same result. It's a shortcut that only works because it behaves as a wave.

Once we open the box, we collapse the wave function, and the particle is essentially picking a random point (probably of each point determined by the wave function) and then the particle is there. If it helps you to think of it as a mathematical trick, then sure, you can have that, but it works like this in the real world or else the single photon double slit experiment and quantum tunneling wouldn't work.