Why do atomic orbitals have their unique shapes?
The pictures that we typically use to represent orbitals are really just graphs showing the 3-dimensional probability of finding an electron (that occupies the orbital being examined) in space.  $\ce{\Psi}$ is the wavefunction that describes the electron with a set of specific quantum numbers.  $\ce{\Psi^2}$, gives rise to the electron density distribution (the shape of an orbital) plotted in the graph.