What does the "emer"setting on my thermostat do

If you have a heat pump, it kicks in the strip heaters, to give instant hot heat. It heats up electrical strips of wiring, and is much hotter than the normal "heat pump" air.
If you have a heating oil furnace attached (like I do), then the heat pump will kick in the oil furnace, giving hotter heat.
The Heat pump is not very effective in temps. Below 32 degrees F, cause there isn't much warm air left in the colder air for the heat pump to bring out.
I am assuming you have a Heat Pump, since you didn't say what kind of heat you have.

"Emer" shuts down the heat pump compressor so you are only using the electric or fossil fuel supplemental heat.