A common question I’ve gotten is what physical meaning the sign of a wavefunction has, especially when comparing the 2s orbital to the 1s. This section of the Wikipedia entry on Atomic Orbitals has some nifty animations that use a vibrating drum head as an analogy.

The wavefunctions that describe atomic orbitals bear some similarity to the physical formulas that describe such oscillations in the real world. For example, look at the s-type modes of oscillation of the drumhead, and compare to descriptions of the 1s, 2s, and 3s atomic orbitals.  Whether the drumhead wave is a crest or a trough is akin to whether the wavefunction is positive or negative. The circular regions where there is no net deflection of the drumhead are analogous to the spherical nodes present in the 2s, 3s, and higher-s orbitals.

Compare the first animation of the p-type modes, and the first animation of the d-type modes, to the depictions of dumbbell-shaped p orbitals and cloverleaf-shaped d orbitals in textbooks. For each of these new modes of vibration, there’s a new planar node.  For the first p-type vibrational mode, there’s a line across the drumhead where there is no net deflection--half the drumhead moves one direction, half the other.  This is analogous to the two lobes of a p-orbital shown with different signs.  The first d-type mode has two node lines at 90 degrees--each quarter of the drumhead alternates in vibrational direction. 

Now, if you could imagine stacking two vibrations of the same type on top of each other, they could either reinforce each other (resulting in increased deflection--a “higher wave”) or interfere with each other (leaving a perfectly flat drumhead).  This is analogous to our model where we add or subtract atomic orbitals to arrive at new molecular orbitals.