How can reducing peak demand for power result in decreased energy consumption?
It can if it changes people's behaviour and/or if more efficient technologies are installed; otherwise, it might not actually decrease energy consumption.
Peak demand for power from homes is usually early in the morning when people are getting ready for school/work whatever and then in the evening during the dinner hour. Industrial users of energy tend to be constant over the workday.
So, if a power company can convince people to, say not leave the fridge door open for 5 minutes in the morning as they look for breakfast, this would reduce the overall energy used per day by that consumer. If you could get a million people to change this one behaviour, it would start to add up to significant energy reduction.
However, if you, say incorporated daily savings time in your country, and the peak demand for power shifted one hour ahead, but people still kept the fridge open for 5 minutes, it would not change the overall demand for energy it would just shift the peak demand ahead by 1 hour.
If you convinced people to all buy energy efficient fridges and they still kept it open for 5 minutes, you would likely still achieve an overall reduction in energy demand if enough people bought them.
Shifting peak demand, or load as its called often, is often of more benefit to power companies than consumers. The one exception might be if., for example, your country used a lot of solar energy - in this case shifting peak demand to the time when your solar panels are producing the most power (and not having to rely on fossil fuel back up plants), might be a good thing in terms of overall energy demand.