A simple answer. A watt meter measures the voltage and current in a circuit and displays (calulates) the wattage. Refer to the source provided by Bjarney, for the how/why these systems work.
The elements of a meter refer to the set of voltage and current measuring windings. Therefore:
2-elements can measure two complete sets of voltage and current. They are used on 3-phase Delta as well as on 1-phase systems.
The 2-1/2 element is used to measure three currents and two voltages simultaneously. These are often used on 3-phase 4-wire systems with balanced phase voltages. This construction has some minor inaccuracies (caused if phase voltages are not equal) but they are usually more acceptable than the cost of a 3-element device.
3-elements can measure three independent voltages and currents at the same time. These are used on 3 phase Wye circuits where the phase voltages are not balanced.