Generally technically speaking (just for a second, bear with me here, it'll come together, hopefully...) a linear process is one where the initial value pumped through the equation/algorithm is an original or independent value each time. One example might be if you took a sample value and then plugged it into the the math to get a result. Then you take the next sample, pump it through the math, and get a second result. Peak normalization would be a good example of this, where you take each sample and add the same amount of gain to each value. Each iteration of the algorithm that the plug runs is independent of the others. That is, the resulting change to sample 5 has no bearing on what happens to sample 6.
A non-linear process is one where when you iterate through the equation/algorithm, the results of the first iteration become the input values of the second iteration. That is, you grab sample 5, run it through the math, and then the next iteration of the math ain't taking the value of sample 6, but rather the value that was the result of the first time you ran the equation. Then you take that result, and churn it through the math again. And so forth for as long as the plug's algorithm is programmed to do it. Then it may or may not move on to the next sample and start all over again, depending upon the program. With reverb, this is kind of obvious, because it has to calculate the bouncing and decay and so forth of more than just the first reflections of the sound. It has to also calculate the way the first reflection bounces a second time off the opposite wall, the way that then bounces a third time off the ceiling, and so forth. This is why really good reverbs are such CPU hogs, there's a whole lot of re-calculating going on.
Because of self-referencing of non-linear math - the using the output of one iteration as the input of another iteration - a lot depends upon the accuracy of the equation's output. The more iterations, or cycles, that the value gets churned through, the more the amount of error will build up. Now it's pretty obvious that a nice floating point plug will allow more digits of accuracy than a standard fixed-bit plug.
I admit that I don't quite know off the top of my head why an increased number of samples should matter. But this post was not meant to answer that, just to define the difference between linear and non-linear processes.
G.