Quantum Mechanics - The Wave Function

It was known that you could describe a quantum system with something known as a wave function. But people didn't exactly know the physical meaning of the wave function because it could take on complex values. Borne's role came and gave more meaning to the wave function by saying that if you square the wave function, you get the probability of finding the particle at that particular state. What this seems to imply is that electrons aren't in one place at one time.