Hi everyone. I'm not an electrician; I'm an electronics tech in Austin, Tx. I hope nobody minds me posting here, even if I do work on the other side of the disconnect (I'm also a homeowner, but at least I know the difference between a codebook and a Sunset Book.)
Appy, RMS is the equivalent DC voltage for an AC supply. I think you're asking why RMS equals .707 peak voltage. This is because pure AC power is considered to be a sine wave. If you average the absolute voltage across one cycle, it will be the peak voltage multiplied by the sine of 45 degrees, which is .707. This makes sense as this is also the voltage at an instant halfway in time between zero volts and a peak.
It might be worth noting that RMS doesn't equal .707 peak for all AC signals. For example an AC square wave, where voltage jumps immediately between positive and negative peak voltage, would have an RMS voltage equal to the peak voltage. It's just that electric power is pretty much kept to a clean sine wave. Here's
a page that explains it pretty well (probably better than I could.) In any case, I hope I helped out with this.