Lately I've been looking at power as an evaluation metric for my research. Power consumption has always been an important design concern in embedded and resource constrained devices. Recently, power has also become important in desktop and server computing environments at the chip-level and at the rack-level respectively.
Energy and power are related, and the two are so often used synonymously that confusing them is quite easy.
Power, typically measured in (kilo)watts, is a rate of production or consumption of energy. The watt unit is an expression of coulombs per second, where a coulomb is a unit of electric charge. So power is the rate of change of electric charge over a period of time. Energy is typically measured in (kilo)watt-hours, which is what shows up on your "power" bill. So you pay for the total amount of energy consumed during the period of your bill, which is actually power integrated over that interval.
A common analogy to help understand the relationship between power and energy is that power is to a flow of water as energy is to a pool of water. The flow can be very slow, dripping even, but can fill a pool given enough time; or the flow can be very fast and fill a pool even quicker. The amount of water in the pool is analogous to energy, and the rate of the flow is analogous to power.
I find it is also helpful to consider the physical equations.
To understand power and energy, think back to middle or high school and recall Ohm's law, I = V / R (equivalently V = I * R), where I is current, V is voltage, and R is resistance. Current is the movement of electric particles, measured in amperes. Voltage is the force required to drive a current between two points, measured in volts. Resistance is opposition to current, measured in ohms. Note that current and voltage are only non-zero if there is a mismatch in the electrical potential between two connected points, and that bad things happen as resistance approaches zero.
Ohm's law is about as far as most people recall (if even that far!), and we haven't yet reached energy or power. We can get some interesting equations by substituting Ohm's law into Joule's first law after some massaging, P = I^2 * R = V * I = V^2 / R, where P is the power dissipated by a resistor. Power dissipation is a more accurate term for the notion of power consumption, although the two can be used interchangeably to mean the conversion of power into some other form of transfer of energy, for example heat or sound. The power dissipation of the resistive elements of a circuit is equivalent to the instantaneous power applied to the circuit in order to generate current through it. By considering a current applied from time 0 to t to a circuit with resistance R, the electric energy created by the current passing through the resistive elements of the circuit during that time interval is E = P * t.
The moral of the story is that power is the rate of transfer of electrical charge, and that energy is an accumulation of electrical charge.