Adjusting the thermostat sends a signal to the compressor that it needs to either increase or decrease its work output. If you want it colder inside, move the thermostat setting to a colder setting, and the temperature inside will slowly adjust to the new setting. In the interim, you'll probably notice the compressor running for a longer period of time as it goes through the process of compressing more refrigerant. If you turn the thermostat to raise the temperature, the compressor will run less often as it cycles less refrigerant.
The compressor does the bulk of the work of compressing refrigerant from a liquid into a gas, which sets off the cooling process that eventually results in a cool refrigerator compartment. Without refrigeration, it only takes a few hours of food being exposed to temperatures above 40 degrees Fahrenheit for it to go bad from bacteria growth. Foods in need of refrigeration and intended for human consumption should be kept below this level, according to the United States Department of Agriculture.
The tricky part about finding the proper thermostat setting for your refrigerator is determining how accurate it really is. Just because you set the dial to 37 degrees doesn't mean that's what the actual temperature inside really is. Sometimes there are leaky seals which let in warm air. With some models, items stored in the door will be a few degrees warmer than those in the back due to the way the air circulates inside. It's a good idea to put an appliance thermometer inside the refrigerator to make sure the temperature is what the thermostat setting claims.
The primary concern when adjusting the interior temperature of your refrigerator is how long it takes. It can take several hours for the actual interior temperature to adjust. If you fall into the habit of switching the dial back and forth, thinking that the compressor is not doing its job, try setting it where you want it and give it 24 hours before you check again. If the compressor is running and you have no refrigerant leaks, the refrigerator will reach an equilibrium around the temperature you desire.