What is actually happening with neuron during refractory period? Sorry for a very rookie question. I've got an interest in spiking neural networks and therefore I started learning about different neuron models like Leaky integrate-and-fire, Izhikevich, etc. But then I became interested in the biological nature of all the processes happening "under the hood".

What I really don't get at this point in time, is what is happening with the neuron while it is in its refractory state? Most of the sources say something like during the refractory period, a neuron is unable to produce new spikes. Yes, I get it. But what happens internally? I.e. how the incoming impulses are handled during this time?

I mean, a neuron is constantly receiving impulses (spikes) from other neurons it's bound with via synapses. So hundreds (or even thousands) of presynaptic neurons will keep sending impulses to our post-synaptic neuron, while it's refracted. What will happen to all these impulses? Will they just become "discarded" somehow? Or will they be still somehow accumulated within the post-synaptic neuron and their influence will be considered later, after neuron comes back to the resting state, in order to produce an action potential? 

Because, if the incoming signals are discarded, then we are losing the "data" in some sense, which I don't believe is happening in reality. If these signals are accumulated somewhere, what's the maximum capacity of this "somewhere"? What happens in case of overflow? And anyway it would mean that the transfer of the signal within the network gets delayed, and that's quite confusing...
Here you are confounding the function of a neuron with its implementation (you might want to read about David Marr's 3 levels of analysis). Functionally you can describe neurons and neural networks using information theory, bayesian modelling, causal networks or any other framework makes sense in what you are studying. However keep in mind that a neuron is a biological object.

There are 2 kinds of refractory periods caused by 2 separate mechanisms (see image from physiologyweb.com). Firstly because the potassium channels are slower than the sodium channels, there is a time after the spike where the cell is hyperpolarized. The electrical potential of the neuron is lower than its resting potential. This is the relative refractory period where it is harder to make a neuron spike (because you need a higher depolarization to reach spiking threshold). This is well describe by the Hodgkin-Huxley model. On top of that the sodium channels themselves have a refractory period. After being activated they remain inactive until the cell become hyperpolarized. This is the absolute refractory period.



To go back to this idea of level of analysis, a model is always a simplification of the world. If you wanted to have an exact model of a neuron you would need to model the ions themselves. Instead if you are interested in the flow of ions you can simply model the gates and their dynamics. If you are interested in the electrical potential you can ignore the gates and use the Hodgkin-Huxley model. If you are interested in the spikes you can simplify it even further and use an intergrate-and-fire model. You can even model only the mean firing rate and so on and so forth. From the point of view of the neuron, or the ions being pumped in and out the neuron, there is no "data" to be processed. All you can say is that it functionally behaves as if it was implementing whatever function you are studying. But keep in mind it will always be imperfect as it is a biological object.