To quote Physics.SE tag definition:
The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.
...and one could add that these systems are usually described by nonlinear differential equations (which prevents the superposition etc.). That's clear.
Now, I need to explain typical features of this behavior without the math. Please note that "explain" does not mean "define", that would be an obvious dead end.
Since this is very broad, let me narrow it down. I need this for a popular lecture about fluid dynamics and turbulence. My aim is not to use sentences like "We have here a highly non-linear flow" without explaining or exemplifying the term.