Can someone give me a brief explanation of what a wave function Ψ is, and

 

how you can derive from Ψ n, l, ml and how it can be graphed, along with

 

\its importance with respect to Schrodinger's model of the atom?

The wave function Ψ is "simply" a solution to the Schroedinger equation. If you've seen it, you know how formidable it is. When you plug the wave function back into the differential equation, satisfies it. To be honest however, the equation has only been solved exactly (analytically) for the case of hydrogen. Perturbation theory is needed for more complex structures and even then it seems impossible-ish.

 

The importance? Schroedinger's equation is the one of the most fundamental mathematical formulae in QM. The fact that the solutions are of wave functions shows the wave nature of matter.