Infectious illnesses are caused by microorganisms like bacteria, viruses, and fungi. They can be spread through coughing, sneezing, or sharing spaces. Non-infectious illnesses have other causes like accidents, toxins, obesity, or cancer. Health is defined as complete physical, mental, and social well-being, while illness impairs one's health. The document provides examples of infectious illnesses like the flu or measles and non-infectious illnesses caused by factors such as poisoning, accidents, or poor diet.