We have a Lennox 27H3101 thermostat. It is making a clicking noise and then stopping. Now, it only says the time and "-AC". I replaced the batteries two days ago.

Earlier today, when we used the slider to select heat, the house filled with white smoke and the breaker tripped. The thermostat still says the time and "-AC". What does that status mean?

On some thermostats the "AC" display means there's either a problem with or no 24 volts AC being supplied to the stat. Since the house filled with smoke, I STRONGLY suggest getting a qualified local HVAC service person to check the furnace.