Illness is usually caused by multiple factors, not just one.
Literal
Illness [topic-は] normally one [not-ではなく] diverse causes [by-によって] occurs.
通常 ('normally, usually') is a formal adverb. ではなく negates '1つ' — 'not just one.' によって marks the agent/cause. 多様な原因 means 'diverse causes.' Written in an informative, expository style.