The value literally is the square root of the mean of the squares of the sampled values. This is of use when a value behaves in a sine wave like manner, allowing usefull averages other than zero to be found, despite the quantity having spending equal amounts of time being positive and negative.
Theoretically this can be shown to be the effective value, i.e. the value of the equivalent direct current that would produce the same power dissipation in a given resistor. For a sinusoidal current this is equal to I0/sqrt(2), where I0 is the amplitude of the current.
Alternate Spellings: root-mean-square