Here's a basic breakdown.
The average or mean setting is the sum of those numbers divided by the number of items.
So, if you have 4 readings of 3, 6, 3, 6, the mean/avg is:
3+6+3+6 = 18
18/4 = 4.5
For RMS, we square the items then take the square root:
3^2 + 6^2 + 3^2 + 6^2 = 90
90/4 = 22.5
square root of 22.5 = 4.74
So, using the average we get a value of 4.5 and using rms we get a value of 4.74.
But why is rms more "accurate"?
Well, Power can also be defined as:
P = V^2/R
From this, you can see that power is proportional to the square of the voltage and not the voltage directly.
There's a better explanation here:
SmartGauge Electronics - RMS volts as opposed to average volts - simple explanation