The wave of the electron is not actually a true wave, but a wave that describes the possibility of finding the electron at a certain location.
When we say that the electron is somewhere on the wave, we meant to say that the electron is simultaneously everywhere on the wave. We can't say that the electron is on a certain position on the wave because then we lose the wave analogy, which means the "wave" is no longer spread out, the wave function of the electron collapses.
When no one is looking
When nobody is looking at the particle, the particle is said to be in a superposition, which means all the possibilities that could happen does happen at the same time. The possibilities are happening simultaneously due to all that the particle also simultaneously exist on every part of the wave.
When someone is looking
However, when someone is looking, the nature has to choose, the particle has been detected, therefore its wave no longer exist, because once the particle is found, there is no need to indicated the possibilities of finding a particle!
Now the location of the electron is set, there is no longer the wave function of the electron, it now acts like a particle!!