Your thermostat is connected to your furnace via a low voltage control wire. This control wire actually has many smaller wires within. Each wire is a different color and controls a different function of the furnace. The blue wire is typically associated with heating and air conditioning systems that have two stages of air conditioning. Two stages mean that at first the air conditioner turns on at a lower setting to try to bring the room to temperature. If that isn't successful after so many minutes, it kicks up to a higher setting until the temperature is satisfied. This method saves money on energy costs. It is fairly easy to wire a thermostat with a blue wire, and you only need a few hand tools.

...
...

Turn the power off to the furnace and air conditioning system. Look for the corresponding breakers and turn them to the "Off" position.

...

Remove the furnace access panel. It should pull off with gentle pressure.

...

Look for the control board on the furnace. On the control board is the terminal strip where the thermostat wires are connected to. Ensure that the blue wire is connected to the "Y2" terminal. If not, connect it.

...

Put the furnace access panel back on and head to where your thermostat is located.

...

Remove the thermostat by pulling it off the wall plate with gentle pressure.

...

Check to see that the blue wire is connected to the "Y2" terminal on the thermostat. If not, connect it. Push the thermostat back on to the wall plate.

...

Turn the power back on to the furnace and air conditioning system.