These points are available when you have multicomponent system and the spectra of the individual components cross each other. If some process happens (protonation, shift of an equilibrium upon temperature, irradiation, etc.) the spectrum changes, but always goes though these/this point. So you cannot have a special interpretation. This point just shows that: a) you have a process or shift in an equilibrium; b) the spectra of the individual compounds are the same in this point.
All discussion above was about isosbestic point. For isoemissive point - the same (switching from one to another component) is valid as well, but there are some exceptions. In the case of emission the availability of isoemissive point can also mean switching of the emission process in a single compound. For instance changing from let say charge transfer to local transfer, so on, by changing the solvent or temperature.