I need to model the popularity of some requested files from a library with Zipf distribution and I want to simulate it in MATLAB. I don't know what's the effect of parameter s on my result. for example, if I choose it greater than 1 or less than one how it can change my result? I've been reading that this parameter determines the shape of the distribution but I don't know what does it really mean. This parameter is something that I should choose in my simulation or it depends on the data that I model?
In every case the probabilities form a decreasing sequence but the rapidity with which they decrease depends on the parameter.
Lower values of the index parameter imply relatively more of the probability is associated with larger numbers ('heavier tail').
If $s\leq 1$ then the range must be finite; if $s>1$ its possible to have a distribution with no upper limit.
This parameter is something that I should choose in my simulation or it depends on the data that I model?
That depends on what you're trying to do. If you're trying to model data then you would (nearly always) estimate it from data; if you're trying to do something with simulation, it would depend on the purpose of the simulation.