The square root of the mean of the square. RMS is (to engineers anyway) a meaningful way of calculating the average of values over a period of time. With audio, the signal value (amplitude) is squared, averaged over a period of time, then the square root of the result is calculated. The result is a value, that when squared, is related (proportional) to the effective power of the signal.
Unfortunately, calculating the RMS value of anything but a simple sine wave (.707 of peak) is very difficult. The further a signal gets in harmonic content from a sine wave, the less accurate RMS values will be. For a dynamic signal like most music, it is nearly impossible to get even close to a true RMS value.
Note: RMS Power is actually a misnomer, since the RMS of a signal is a really just a value used to calculate average, or continuous, power.