Energy rush hours occur when all houses in a geographic area turn the air conditioning on at once. When so many air conditioners are activated at one time it creates an energy demand peak. Combined with all other energy uses in homes this peak demand can cause utility companies to bring seldom used power plants online to meet the need. Those seldom used plants are costly to run especially when they are only needed for a short time and those costs are passed on to the consumer. By taking part in a Nest Rush Hour you contribute by using less energy during those peak times which utility companies are willing to reward you for.
Once you sign up to participate the Nest thermostat will automatically change temperatures leading up to and during the rush hour period to use less energy. If you get uncomfortable you can always override the temperature. Every energy company handles the rewards for consumers differently so you will want to check with them for specifics.