Basically, if there are any electronic states that don't deactivate via fluorescence this will cause the excitation spectra to differ from the absorption spectra. E.g., absorption into a higher lying electronic state that undergoes photochemistry that is competitive with internal conversion to the lower-lying, emissive state. Nonlinear absorption effects or polarization effects can also lead to this phenomenon, and it can also be observed with fluorophores that explore a large conformational space, if the excitation band is sufficiently narrow in bandwidth. These are the first things that come to mind, but certainly there are others.