Peak demand is the maximum level of power demand (i.e. MW, GW etc.) occurring in a power system. It’s usually stated in the context of a particular period (peak demand during a particular day, peak summer demand, annual peak demand etc.). Since it’s a measure of power, it is also specific to a particular point in time: e.g. “peak demand during 2014 occurred at 5pm on November 20th”.
The central economic importance of peak demand is that it determines the amount of capacity that the system needs to have available, in order that the lights don’t go out at these peak times. Yet because the amount of time the system spends close to or at peak demand is often relatively small, much of that installed system capacity isn’t needed for most of the time (but still needs to have a business case to stay available).
In particular, electricity at times of peak demand is supplied by generating resources which operate very infrequently (but must be maintained and kept ready) and are generally the least efficient or most expensive supplies in the system. As such, infrequent periods of peak demand can have a disproportionately large impact on the overall costs of electricity generation, as a result of large price spikes when peaks occur.
Demand response agreements are one important way of reducing the economic impact of peak demand, by reducing demand when it starts to peak rather than maintain and schedule expensive, short-lived supply options. On the supply side, where it’s difficult to create an investment case for power plants that will operate very infrequently, mechanisms such as capacity markets are being used to guarantee reliability of supply, paying on the basis of MW availability rather than MWh of generated energy.