The compressor of an air conditioner is a bit like a small electric motor in that it has gears and turning parts that require lubrication. The lubrication in the air conditioner compressor comes in the form of oil, typically located in the compressor case itself. When an air conditioner is turned on its side, this oil settles on the bottom half of the compressor and potentially deprives part of the compressor of oil, which can lead to damage and, eventually, compressor burnout.
Window air conditioners, just like all other air conditioners, dehumidify the air to improve indoor comfort. The air conditioner pulls in indoor air and blows it across cold copper coils filled with refrigerant. These coils "sweat" the humidity in the air in the form of condensation. This condensation drips, through gravity, down into a condensation pan. If an air conditioner is positioned on its side, this water will drain down into the case, potentially damaging the unit and leaking water back into the home.
Air conditioners have ventilation grates, or fins, on the sides and bottom of the unit, which allows sufficient airflow in to the hot side of the unit, allowing for the dispersal of heat removed from the home. If an air conditioner is situated on its side, rainwater will drain into these grates and damage delicate internal mechanisms.
If an air conditioner has been stored on its side, or when receiving an air conditioner that has been shipped, take care to ensure it has been turned horizontally for a period of at least 24 hours prior to running the unit, which allows sufficient time for any oils and lubricants to resettle back to their proper levels, providing protection for internal gears and moving parts.