Why does an inductor offer high impedance to ac but very low impedance to dc?

Because an inductor resists a change in current. The equation of an inductor is ...

di/dt = V/L

... meaning that the rate of change of current is proportional to voltage and inversely proportional to inductance. Solve the differential equation in a sinusoidal forcing function and you get inductive reactance being ...

XL = 2 pi f L