# What is the interpretation / intuition of a lipschtzian function?

What is the interpretation / intuition of a lipschtzian function? I mean, a continuous function is one that "does not show jumps", what is the significance of a function being lipschtziana?

It is one that does not become arbitrarily steep. $\frac 1x$ becomes steeper than any given slope as $x$ approaches zero. It is not Lipschitz.