What does maximum frequency range really mean in an inductor?
It is the frequency range over which it meets its stated specifications. Outside that range, parasitic effects start to become significant; with inductors, the primary problem is the distributed capacitance among the windings, which creates a parallel-resonant circuit that causes the impedance to rise anomalously near resonance.

If the inductor has a core, losses in the core can become significant, too. This appears as an effective resistance in parallel with the inductor, reducing its "Q" or quality factor.