>>13539796I mean that the effective mass is the apparent mass an electron has in a solid when you employ certain semiclassical models. Such an effective mass allows one to have simplified equations of motion. Often, electrons in a solid behave like as if they were in a vacuum, but with a modified mass.
This should illustrate that in interacting models, often one can employ effective reparametrizations of the model, which are valid at certain energy/length scales. From a macroscopic point of view, it's a very good approximation to just assume the electron has some increased mass, as for some constant applied force a higher mass means smaller velocity. Of course, if you are interested in the detailed dynamics at the scale of say the lattice constant, just giving the electron a larger mass is a rather poor description of what is really going on.
This is the main idea of the modern formulation of renormalization/effective theories as employed in statistical mechanics, statistical field theory/quantum field theory. Take for example a pion as the force carrier of the nuclear force. This is a very valid model for strong interactions at energy scales typical for a nucleus. For higher energies, however, this model gives you garbage results, because you left it's range of validity. A more fundamental model has to be used, which is Quantum Chromodynamics.
