Sorry for my ignorance, but does the result of Michelson-Morley experiment have some explanation? Is there some reason why light speed in vacuum is maximum or we just find it by experiments?
We just find this by experiments. It is a property of the spacetime that there is some maximum speed. It is not just the speed of light, but the speed of all massless particles. We don't kow why spacetime behaves like that.
Please note that if nature would work differently (there would be no maximum speed), we would not know why that is the case either.
The special theory of relativity's axioms are essentially the same as those that underlie Galilean relativity - please see my answer here for further explanation of this statement - the difference is that in Galilean relativity these assumptions uniquely define the transformations between inertial frames whereas STR relaxes the assumption of absolute time, which means that the transformation is no longer uniquely specified but instead is parameterised by a universal constant $c$ with the following crucial properties: an object moving at this speed will (1) be observed to be moving at this speed in all inertial frames and (2) must be massless (the latter is not as fundamental as the first, but it can be shown that the transformation laws imply a massive object would need infinite energy to reach $c$). Further reasoning shows that all massless particles must move at this universal speed $c$. So the postulates of relativity are the axioms, and the speed which is the same in all inertial frames is a concept that is derived from these axioms.
So then, a modern interpretation of the MM experiment is that the speed of light is observed to transform in the way foretold by the reasoning above, i.e. its value is the same for all inertial observers.
Conclusion: light is mediated by a massless particle, and therefore we can experimentally measure the universal speed parameter $c$ by measuring the speed of light.
WItness how, from this standpoint, a positive result to the MM experiment (i.e. that lightspeed depends on observers) would NOT needfully contradict special relativity. At least, not directly. A positive result could be interpreted as the photon's having a nonzero mass, and we'd be left looking for some other particle's motion to tell us the value of $c$. And it could still be that $c$ would be infinite: for Galilean relativity is indeed consistent with the postulates of special relativity. Notice how we ken $c$ when we see it: the important thing is NOT its numerical value, nor that it pertains to light or anything else in particular. The crucial thing is how this speed transforms (or doesn't) between different inertial frames.
However, the photon's mass can be bounded by other means, e.g. by measuring electric fields inside hollow conductors, and we know it is exceedingly low: see my answer here for further details. So, from these other photon mass measurement experiments, we know that light must move at very near to $c$ (reasoning backwards: STR implies massless particles must move at $c$). So in practice, modern physics and special relativity would be in for a bit of a shakeup if someone's reproduction of the MM experiment turned up a positive result, unless the observed dependence of lightspeed on frame were small enough to be consistent with the upper bounds on the photon mass that we find from other experiments like the field-in-hollow-conductor experiment (as well as others - see the Wiki Page on the Photon and the section called "Experimental Checks on Photon Mass").