Demand response is simply what is sounds like, the response to an increase or decrease(change) in demand. There are two types of demand response, electrical and economical. I will only be talking about the electrical portion, and about how and why demand response occurs.
The definition of demand response by the FERC(Federal Energy Regulatory Commission) is as follows :
Changes in electric usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized.
This tedious definition simply says that by changes in the price of electricity or during times of high or low energy needs, the demand by customers may vary.
Demand response usually pertains to times when energy use is extremely high and there is not sufficient supply to deal with the intense demand. When this happens there can be power interruptions and sometimes even total blackouts altogether. For example, in southern California during a hot summer day demand may be near an all-time peak. Because of this, power plants may be reaching their output maximum and if the demand is too high then power interruptions or blackouts could occur.
There are solutions to this problem. The first obvious answer is to build more power plants to be able to cope with any amount of demand during periodic high peaks. However, this is not environmentally friendly and the cost of producing enough new plants would be huge. Also, these power plants would be virtually useless and a waste during times when there are not energy shortages, which is the most of the time.
The most popular solution to demand response is for many local business and volunteer programs to reduce their demand for energy when supply is low, therefore putting less stress on power plants to do their jobs. If enough organizations participate in this then the entire problem of having too much demand and not enough supply could be alleviated by spending no money at all.
Sources:
http://www.pge.com/mybusiness/energysavingsrebates/demandresponse/whatisdemandresponse/
http://www.ferc.gov/industries/electric/indus-act/demand-response/dem-res-adv-metering.asp
http://www.drrc.lbl.gov