Demand is measured in units of power, most notably in KW (for electrical use). It is uncommon for a residence, but for commercial buildings, Utility companies may charge for the peak demand use.
Example:
The general analogy used for demand is a car. Demand is equivalent to the car's speed, while consumption is equivalent to the car's odometer reading (distance travelled). It is not uncommon for a utility company to penalize a customer for having a very high demand - this could be considered similar to a speeding ticket (financially of course, because high electric demand isn't a crime, at least not yet)