Lipschitzness is a noun coming from the term Lipschitz continuity.
A Lipschitz continuous function is simply a function that has a limit on how fast it can change.
The Lipschitz constant of a function is a number that defines this limit. If the function is Lipschitz continuous it cannot change faster than this constant (the absolute value of the gradient is always smaller).
In the image below, the function can never cross the white cone - this is the limit of the change the function can make.
Image source: Wikipedia