RMS, or "Root Mean Square" (also called effective), voltage is a method of denoting a voltage sine waveform (AC waveform) as an equivalent voltage which represents the DC voltage value that will produce the same heating effect, or power dissipation, in circuit, as this AC voltage.
In other words, the waveform is an AC waveform, but the RMS value allows this waveform to be specified as if DC, because it is the equivalent DC voltage that delivers the same amount of power to a load in a circuit as the AC signal does over its cycle.
AC and DC waveforms can both represent voltage or current waveforms, but they are in different forms. AC waveforms fluctuate between positive and negative voltage in cycles. DC voltage is just constant one-way voltage that doesn't have cycles. Because of this difference, it's very difficult to compare the two.
This is where the RMS value is important. It gives us a standard to compare the amount of power that an AC waveform and a DC waveform can give to a circuit. RMS voltage is the DC equivalent of an AC waveform so that we can compare power dissipation with both the AC power and DC power waveforms. If we have a RMS waveform of an AC signal and it it is the same value as a DC waveform, then we know that both waveforms give off, or dissipates, the same amount of power in a circuit.
The reason RMS voltage is also called effective voltage is because it is just as effective as DC voltage in providing power to an element (it's equally effective). Since RMS voltage is the DC equivalent voltage, the RMS voltage is just as effective as its equivalent DC voltage in providing power to an element or load in a circuit.
In audio RMS is the measurement of the average amount of voltage used to power an audio source to where it will reach a threshold of THD or "Total Dynamic Distortion". It is typically called RMS power rating, or simply just RMS rating (often denoted as Watts RMS).
When you hear "RMS Power" (as opposed to "Peak Power"), that is the amount of power that a loudspeaker or a sound source can typically handle over a period of time without producing any audible distortion, or produce a THD level below a certain accepted threshold (usually <0.5%). It is also used to measure the amount of power that an amplifier will send to a speaker or sound source.
RMS is generally the standard used to measure how much power a loudspeaker can handle. So if you want a louder loudspeaker, choose one with a higher RMS rating. Similarly, make sure you have an amplifier that has at least the same amount of RMS power or more.