To save money on your electric bill. A smart thermostat will know when you’re not home, and automatically turn up the temperature to keep the bills down. It can also know when you’re heading home, so that it can turn it back down and have the house already cooled for you before you even open the front door.
You can also use them to automatically pre-cool your house at night, when electricity is cheaper. The residual coolness keeps temperatures down and the thermostat doesn’t have to run the A/C as much during the day, when electricity is more expensive