Nonfeasance (literally, "doing nothing") means that an act required under a statute was not performed.
When statutes require an action on the part of a person, group or entity, failure to take the required action leaves the party in question subject to legal sanctions, including monetary fines and imprisonment. For example, a corporation required to dispose of toxic wastes in a manner prescribed by the Department of Ecology that instead simply dumps the wastes into a river has committed an act of nonfeasance. The corporation may be subject to fines, and if the omission (failure to act) is particularly egregious, the corporation may be dissolved or its charter revoked (analogous to being put to death).
Nonfeasance by itself does not necessarily imply that malice (evil intent) was involved. Sometimes, it is no more than an oversight, the consequences of which caused hardship or injury. For example, Bob at Bob's Used Cars takes action to repossess an automobile purchased by Dale, who has fallen behind in his payments. Dale subsequently gets a better job and pays Bob the entire outstanding balance. Bob however neglects to provide a receipt for payment and forgets to cancel the tow order. As a result, Dale has nothing for the repo man to prove that vehicle is paid for. The car is towed, and by the time Dale straightens out the mess, he has missed two days of work (and therefore, income).
Bob was legally obliged to provide a receipt. The fact that he failed to do so constitutes nonfeasance, making him liable should Dale choose to pursue legal action in order to recover his lost wages as well as damages for psychological harm and inconvenience.
Nonfeasance should not be confused with malfeasance, which is willful misconduct or omission with intent to cause harm, or misfeasance, which suggests ignorance of statutes.