From an article titled "Characteristic Impedance of Cables at High and Low Frequencies" on the Belden website at
http://bwcecom.belden.com/college/college.htm
"Theoretical Definition of Characteristic Impedance
For the moment, imagine that a cable has infinite length. Application of an alternating voltage to this infinitely long cable would allow a measurement of current and calculation of impedance (both magnitude and phase). Of course, there is no such thing as an infinitely long cable. The concept is introduced to promote the idea of a cable which is so long that the signal never gets to the far end. The impedance measurement in this case would yield the impedance of the cable itself, or its characteristic impedance, and not the combination of the cable impedance plus the effect of conditions at the far end. The phase angle would be zero or negative (between 0 and -45o). Recalling circuit theory, a negative phase angle indicates that at the specific frequency at which the measurements were taken, the cable resembles a capacitor with a resistor in series.
Calculations of an equivalent capacitor and resistor to replace the infinitely long cable could be made. Replacement of the cable in the test circuit by these two components and application of the test voltage would result in the identical current and phase angle as observed when using the cable. As long as the frequency of the applied AC voltage does not change, impedance measurements would be identical for both the capacitor-resistor combination and the infinitely long cable.
If the infinitely long cable is cut to some finite length and the far end of this cable is connected to a capacitor-resistor combination which is assembled and found to be equal to the characteristic impedance, an astounding discovery is made. The impedance measured looking into the cable which is terminated at the far end with its matching characteristic impedance (the capacitor-resistor combination) is still the same as it was for the infinitely long cable! Cut the cable to any length and if the termination at the far end is unchanged and the frequency is unchanged, no difference in the measured impedance will be noticed."
So characteristic impedance is useful in systems where the frequency is specified like digital audio/video or RF, allowing components to be designed with much less concern about the cable lengths connecting them. It doesn't really mean anything when used without a specified signal frequency as in analog audio.