When an isosbestic plot is constructed by the superposition of the absorption spectra of two species (whether by using molar absorptivity for the representation, or by using absorbance and keeping the same molar concentration for both species), the isosbestic point corresponds to a wavelength at which these spectra cross each other.
A pair of substances can have several isosbestic points in their spectra.
When a 1-to-1 (one mole of reactant gives one mole of product) chemical reaction (including equilibria) involves a pair of substances with an isosbestic point, the absorbance of the reaction mixture at this wavelength remains invariant, regardless of the extent of reaction (or the position of the chemical equilibrium). This occurs because the two substances absorb light of that specific wavelength to the same extent, and the analytical concentration remains constant.
For the reaction:
the analytical concentration is the same at any point in the reaction:
The absorbance of the reaction mixture (assuming it depends only on X and Y) is:
But at the isosbestic point, both molar absorptivities are the same:
Hence, the absorbance 
does not depend on the extent of reaction (i.e., on the particular concentrations of X and Y)
The requirement for an isosbestic point to occur is that the two species involved are related linearly by stoichiometry, such that the absorbance is invariant at a certain wavelength. Thus, ratios other than 1-to-1 are possible. The presence of an isosbestic point typically indicates that only two species that vary in concentration contribute to the absorption around the isosbestic point. If a third one is partaking in the process, the spectra typically intersect at varying wavelengths as concentrations change, creating the impression that the isosbestic point is out of focus, or that it will shift as conditions change. The reason for this is that it would be very unlikely for three compounds to have extinction coefficients linked in a linear relationship by chance for one particular wavelength.