If your illness is caused by bacteria, you can describe it as bacterial. For example, a lung infection that results from being exposed to bacteria is called bacterial pneumonia.
Some infections and illnesses are caused by viruses, and they're called viral. Other kinds occur when your immune system is invaded by microorganisms called bacteria, and these are bacterial. You're most likely to hear the adjective bacterial when you're sick. The root word, bakterion, is Greek for "small staff or rod." Bacterial organisms were named this way in the 1830's because the first bacteria observed through a microscope were rod-shaped.