With a thermostat, smart or dumb, you set a target temperature and a time. With a dumb thermostat it waits till that time and then activates. With a smart thermostat it should learn how long it takes to heat or cool to that target temperature in certain conditions and then aims to hit the target at that point.

So if you got up at 8am and wanted it 20c with a dumb thermostat you got to work out when it needs to go on in order to hit that as no heating system is instant on something the size of a house, with a smart thermostat with learning you do not need to do that at all, just set it for 8am.

As no system is working in a vacuum how hot or cool it is outside, even how sunny it is, has a big impact on how quickly your system heats or cools. Being able to measure and compensate for the outside temperature means the actual start time can be adjusted for you. This can save significant amount of cash.

As an example, lets say the outside temperature was going to be -10c 6am till 8am and you wanted it 20c by 8am. Doing it with a dumb thermostat you would either have to live with an under or overshoot on temperature. Say next day its 2C, now you need to adjust your overshoot again. With a smart thermostat I do not need to do that at all.

Sure, you can just live with the under/overshoot, but its better for your bills and better for the environment not to.