A failure is:
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found in the software; the result of an error.
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departure from specified behaviour
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an incorrect step, process or data definition in a computer program.
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a human action that produces an incorrect result.
A failure is a departure from specified behavior, meaning the software does not perform as defined in requirements or specifications. This distinguishes a failure (observable incorrect behavior) from an error (mistake in code) or defect (flaw in the code), and from human mistakes that cause these issues.
By standard testing terminology (ISTQB), a failure is a departure of the software's actual behavior from its specified/expected behavior during execution — it's what's observed by a user or tester. 'Found in the software; the result of an error' and 'an incorrect step, process or data definition' describe a fault/defect (the underlying flaw in code), not a failure (the visible symptom). 'A human action that produces an incorrect result' describes an error/mistake (the human cause), which is a different concept in the fault-error-failure chain. Only 'departure from specified behaviour' precisely matches the definition of failure.