Thermostat installed, but why also install a separate timer?
Heating practices and equipment vary from place to place. Your setup looks like it is probably in the US but I can give an answer that relates to UK heating. It may be that the same principles apply.
A typical UK heating system is controlled like this
Timer --> Thermostat --> Zone-valve --> Pump & Boiler (furnace)
If you are a working family, you don't need heat in your home when you are at work elsewhere. You therefore set the timer to provide heat in the mornings and evenings.
During those periods, the timer provides power to the thermostat. If the temperature is low, the thermostat provides power to the zone valve (through a relay). Once the valve is open, it provides power to the pump and boiler.
So the timer determines when the house is heated (i.e. when people are present and active) and the thermostat ensures the boiler and pump do not operate if the temperature is already high enough.
There are additional complications if you live in a climate where air-conditioning is needed to cool the house in summer. But the basic principles outlined above probably apply.