Power is the measure of electrical work (or the conversion rate of electrical energy). Power is measured in watts.
P = IE (Power = Current times Voltage)
P = ΔW / Δt (Power = Work over time)
The power consumed in an electrical circuit is proportional to the current of the circuit by the formula P=IE, when you take into account Ohm's Law E=IR you can also find that power is also proportionate to the resistance (or impedance) of a circuit.
Lamps come in different power ratings, however this is not necessarily proportionate to the light output of the lamp. Lumens are used to measure light output.
Power is also proportionate to the Horse Power of an electric motor.