I'm always intrigues by these discussions. How about five examples
of each. It will help me understand where you're coming from.
Almost every linear narrative will be divisible into an act structure. The most basic being "2 acts" - beginning and end. The fundamental of any narrative is 1. introduce the characters and the situation, 2. explore how the situation develops as the characters interact, and 3. show how the situation resolves. You can, of course, put infinite divisions, transitions, etc. into that basic narrative. What tends to make this linear is that time moves in one direction. The plot moves in one direction.
Nonlinear narrative, when pulled off well, gives a whole new sense of timing. Often the viewer is following multiple storylines, taking place at different times, sometimes the events happen in different orders or the writer/filmmaker invokes alternate realities that blur over. It really takes an A-list writer/director to make it work successfully.
Classic non-linear films:
David Lynch's "Mulholland Drive"
Chris Nolan's "Memento"
Bruce Rubin's "Jacob's Ladder"
Eric Bress' "Butterfly Effect"
Terry Gilliam's "Adventures of Baron Von Munchausen"
Television does it all the time. Some examples would be "Twin Peaks" or "Lost" where time and reality seem to bend and blend. There was a brilliant episode of CSI (Vegas) where there were three crimes and we start near the end of the day, then rewind to see how the event unfold and are intertwined. Then at the end, it all comes together.
Non-linear stories have a meaning only after everything has been seen. The whole is greater than its parts. After watching it, the viewer will recall, "Oh, that's why that was important." Linear stories tend to be "predictable" and require 'twists endings'.
It doesn't mean that there aren't linear elements in a non-linear narrative. A non-linear story itself just doesn't have an easily defined "beginning" or "end" or defined "direction of plot evolution". They may have stories within stories that bleed over into each other making reality less defined.
Anyway, that's how I would characterize non-linear.