It is useful because it enables us to quantify our assumption that asmall change in the input made by an algorithm such as gradient descent will have a small change in the output.

University of Michigan - Ann Arbor

A Lipschitz continuous function is a functionfwhose rateof change is bounded by a Lipschitz constant $L$:
$L = \forall x \forall y. |f(x)-f(y)| \leq L ||x-y||_2$

Lipschitz Continuous

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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