There is nothing mysterious about a wave function. The position and momentum of your every day harmonic oscillator (weight on a spring) are described by a wave function that is very similar to Schrodingers Wave Equation for subatomic particles. The major difference is that the SWE incorporates imaginary numbers in its formulations and describes not the actual position and momentum of the particle but only the probability amplitude of the position and momentum. In order to get rid of the imaginary component you have to multiply it by its complex conjugate (square it) which gives you the actual probability of finding the particle at certain position. This is a very large subject. I suggest you think about it and ask some specific questions and I will see if I can help.