How do I explain to my daughter what it means to have atypical pneumonia?

Simple is best. Just tell her she ended up catching some germs that decided to live in her lungs for a while. She will get better with treatment.You needn't be rattles by the "atypical" label, it has no bearing on success of treatment, its just part of medical lingo.
She should relax. Atypical pneumonia is sometimes caused by a bacteria, and sometimes by a virus. It's a more benign type, and often caused by stress. What does her doctor say?