Power is the rate at which energy is generated (in a power plant) or consumed (in an end-use device). In electricity systems, power is expressed in Watts (or typically multiples of this: kW, MW and so on).
It’s worth noting that although we talk about “power generation” and “power plants”, the business case for these projects is almost always based on revenues derived from selling units of energy (MWh) rather than power. Power plant capacity (in MW) simply refers to the maximum rate at which a plant can generate energy: the actual rate will vary according to market need or – in the case of solar or wind farms – the availability of the natural resource (the weather, day/night).
Some power plants can also be paid for guaranteeing to provide energy at a certain rate (power) at peak times, either as part of a power purchase agreement or through a capacity market mechanism.
As consumers, we also buy electricity based on energy usage (usually expressed in kWh) rather than power. Of course higher power devices use energy at a faster rate and so increase our electricity bill more rapidly.
Power is an instantaneous measure, since the rate of energy generation or consumption can vary moment to moment. Dividing energy (MWh) by the time (h) over which it was generated/consumed gives a measure of average power over that time period. The relationships between power, energy and time are also captured by metrics such as capacity factor and full load hours.