How does the thermostat work with the air conditionerc

A thermostat is a switch. It can be a switch attached to a complex computer system, but at its heart is a switch that determines whether the compressor and fans of an air-conditioning system are on or off. It is not a throttle to change the speed or cooling capacity of the air conditioner. This is why setting the thermostat on a cooler setting, such as 60°F(usually the lowest setting) will not result in faster cooling. What it does is instruct the air conditioning compressor to continue working until that temperature is reached. You don't receive cooling faster, instead, you make the compressor work longer.

Why is this wasteful and bad for air conditioning.

You don't want it to be 60 degrees in your house. It's too cold to be comfortable indoors. Your home will be uncomfortable and waste 25 percent more energy if you turn the air conditioner up to 60 degrees Fahrenheit or some other lower temperature. This also forces the compressor to run for longer periods of time, accelerating wear and tear and potentially leading to premature system replacement or emergency failure.