Electronics-Lumped Components

In a very simplified answer, a current flowing through a wire sets up a magnetic field. If the current begins to change, that magnetic field will induce a voltage to oppose the change in current. Inductance is a measure of the coil's capacity to generate that voltage. Inductive reactance is a measure of the actual resistance to change in current. The quantity that causes the reactance to vary is the rate of change of the current (frequency).

For a more mathematically detailed explanation, Google Hyperphysics, go to Electricity and Magnetism and follow the path down to Farady's Law.