It refers to the establishment of the coils...
Regular springs have evenly spaced coils throughout the entire spring
Irregular springs have variable coils. Usually around the two ends are evenly spaced BUT the middle is either spaced further away or closer together.
**It's not a spring, but look at the concept**
Non-linear springs don't really have a pattern, they're typically tightly coiled on one side, get a bit looser, then can tighten up again but not as tight as the first end.
I've yet to know how true this is, but apparently, the idea is non-linear and irregular spring compress better and easier in comparison to regular springs. Apparently this can be better seen/noticed with heavier springs.