Can someone explain to me what the wave function of an electron is? And if possible use plain English without the complicated math which is involved .

If you know what the geometrical optics is and how it is obtained from the wave equations, then it is easy to understand the de Broglie idea that the electron is also a wave with short wave-length, so it is often seen as a particle with a certain trajectory but in fact it is a wave spread in space and the Schroedinger equation is the corresponding wave equation.

The equation that lets you find what state the electron is in, e.g. expected location, energy

Thanks a lot!