An AC waveform, at least from the mains, is sinusoidal. The power delivered is an average over the whole cycle of Voltage, which goes from + peak, through zero, to a - peak. The average value of Voltage is zero - which doesn't tell you much about the peak values. To work out the 'effective' Voltage to get power delivered to a load, you need to add up (integrate) the energy delivered at all stages in the waveform.
One formula for power is P =V2/R.
If you average this over the whole cycle for all instantaneous values of V and average it, you get the 'mean square' value of the Power. Rearranging and taking the square root of this gives the 'Root Mean Square' (RMS) value of the varying Voltage. For a sinusoid, the RMS value is the peak Voltage/(Root 2). The relationship is different for other shapes of waveform.
This RMS Voltage produces the same power from a resistor (lamp / heater etc.) as a DC Voltage of the same value.