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 - the system doesn't behave as documented in requirements. This is distinct from an error (human mistake) or defect (code issue).
In standard software testing terminology (ISTQB), a failure is an observable deviation of the system from its specified or expected behavior — i.e., what the user sees go wrong. An error is the human mistake that causes a fault (bug) in the code, and the fault itself is the incorrect step or data definition. "Found in the software; result of an error" describes a fault, not a failure.