How do genes affect illness?

A gene is a segment of DNA that carries the instructions for a specific trait, such as eye colour or how well you can digest food.  When DNA is damaged or is copied incorrectly this changes the gene and so the instructions may not produce the same trait.  For example, hair colour may be slightly different, or food may not be digested correctly. In many cases, small amounts of damage to DNA will not cause illness, but if it is an important part of a gene, then even a tiny change can have a major impact on health. 

A good example is Cystic Fibrosis.  A small change in the gene that holds the instructions for a small protein which pumps chloride ions across our epithelia (lining of our airways and gastrointestinal tract) causes the production of very thick mucous and damages the way our digestive organs work.  This leads to lung disease, poor nutrition and some other unpleasant symptoms.