What do the signs on an orbital represent?
The signs are the phases.
Each orbital is a construct brought about by the electron. Besides being a particle, since an electron is also a wave, an orbital can be represented by a wave function.
Therefore, an orbital has the properties of a wave as well:
- constructive interference with same-sign overlap, i.e. addition of amplitudes along the wave
- destructive interference with opposite-sign overlap, i.e. subtraction of amplitudes along the wave
With orbitals, it's not necessarily obvious how the overlap results since the waves are complicated, but in general, we at least know that the signs are the phase of the orbital, the literal sign of the wave function.
For example, a hydrogen-like atom has
#psi_(1s) = 1/(sqrtpi) (Z/(a_0))^"3/2"e^(-Zr"/"a_0)#