How does the redox of a battery happen? I tried to understand how does a battery work. After doing some research, I knew chemical reactions inside are key. But when I came across the reactions inside a zinc carbon battery, almost all websites say "Zinc is oxidized and gives out two electrons". 

Why does this reaction happen in the first place? Is it the result of the reaction between the electrolytes and the zinc? And I'm confused what exactly do electrolytes do because I saw they are described as "catalyst". I only understand they allow the flow of ions but prevents the flow of electrons.

Thank you and if what I say above is wrong, please correct me.
The zinc-carbon cell uses a zinc anode and a manganese dioxide cathode. It is manganese dioxide that takes part in the reaction, not carbon. Carbon is added to the cathode to increase conductivity and retain moisture(catalyst). It also contains a layer of ammonium chloride. Following is the overall reaction.
$$ \ce{Zn(s) + 2 MnO2(s) + 2 NH4Cl(aq) → Mn2O3(s) + ZnCl2 (aq) + 2NH3(aq)} $$
This is why the half reactions are as follows,   

Anode: $\ce{2Zn -&gt; Zn^{2+} + 2e–}$

Cathode: $\ce{2NH4+ + 2MnO2 + 2e– -&gt; Mn2O3 + H2O + 2NH3}$   

An electrolyte is a substance that produces an electrically conducting solution when dissolved in a polar solvent, such as water. Here, ammonium chloride solution acts as the electrolyte immobilized in the form of a paste. Basically its a chemical medium for flow of charge.