This type of electrode (inert) such as platinum and carbon is used when the reactants and products in one of the half cells are both ions, gases or liquids i.e. they aren't metals. Like think about it physically how can you have an electrode that is made out of an ion or a gas its not possible.
So what this electrode that is inert basically does is it just provides a surface upon which the reaction can occur, so that electrons can be transferred to that cell from the anode one to allow the stuff in the cathode to undergo reduction. I say electrons are transferred to this inert electrode because if its inert its less reactive than the other metal electodr and therefore becomes the cathode. Common examples where this type of electrode is used include reacting Fe 3+ to Fe2+ and cl2 to cl-, as you can see in both cases the reactants and products aren't something that can form a solid electrode. Apart from the providing a surface for the reaction to occur the inert electrode does nothing to the voltage value or anything like that
