The failure to perform an act that one is legally obligated to do. It's passive wrongdoing—not doing something you're supposed to do rather than actively doing something wrong.
From French 'non' (not) and 'faisance' (doing), literally meaning 'not doing.' The term developed in English law to categorize different types of breaches of duty, distinguishing passive failures from active wrongdoing.
Nonfeasance can be just as deadly as malfeasance—a lifeguard who simply doesn't show up for work commits nonfeasance, but the swimmers who drown because of their absence are just as dead as if the lifeguard had actively pushed them in!
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