Your milk and chicken both have bacteria in them. If you leave them at room temperature, those bacteria will grow rapidly. Some may produce toxins that will not be inactivated by cooking. The greater the dosage of these bacteria, the more likely they are to make you sick. Keeping stored food cold (below 40°F / 5°C) is an important part of basic food safety for reducing the risk of foodborne illness. Now, this doesn't mean that you will always get sick if you eat or drink milk or chicken that has been at room temperature for too long, but it does mean you will be more likely to get sick. Beyond health and safety, you will immediately notice the difference if you put a closed container of milk on the counter for 24 hours, and put another one in a cold refrigerator for 24 hours. You can run this experiment on your own (just don't drink the milk you left out).
You can read more about the importance of refrigeration at various public health websites. Here, for example, is some good information from the US department of agriculture.