[GordMay]

If you just measure the RMS Voltage and RMS Current and multiply them, you get the Apparent power.
As long as the load is purely resistive, the apparent power is equal to the active power.

For any reactive load (usually inductive, such as /w motors), where the Voltage and Current are out of phase, the Apparent power will be greater than the Active power*.

Measuring Active power is a bit tricky (especially /w non-sinosoidal waveforms), and is traditionally done by a watt meter (or more commonly a watt hour meter, like that measuring the electrical energy consumption of your house). Watt meters (and watt hour meters) instantaneously multiply the voltage and current and integrate the result, so they measure true Active power.

* True Active Power = cos (theta)* x Apparent Power
* cosine of the phase angle between voltage and current