A nonstandard model of Peano arithmetic is a model not isomorphic to the standard natural-number structure. It contains the standard numerals as an initial segment and also contains elements larger than every standard numeral.
The standard cut is the external initial segment consisting of the interpretations of the standard numerals. It is not definable, even with parameters, inside the nonstandard model.
If a definable property in a Nonstandard model of Peano arithmetic holds of every standard natural number, then it holds of some nonstandard element. Equivalently, a definable set containing the entire standard cut of a nonstandard model of arithmetic must overspill beyond it.

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