I am considering buying an electric bicycle using brushless DC Hub Motor. What is the difference between 24V Vs 36V motor? Is it related to the maximum torque produced by the motor? If yes, what does that mean to a bike rider?
As far as motors go, usually the higher the voltages the more efficient they run. However there is a trade-off because usually the higher the voltage, the less efficient the battery is! Different systems may balance these factors at different points depending on how they expect the system to be used and what parts they have access too. I don't think you will be able to strictly say one is better than the other, you will need to compare the specs and a whole package and figure out what package suites you best.
Again, it's the same as with battery powered power tools. Usually the higher the voltage the more powerful the motor is and the higher battery Volt-Ampere-hour (not Volt-Ampere alone) rating is.
More powerful motor will usually (but not necessarily) mean higher torque and that will mean climbing steeper hills at higher speeds and accelerating faster. Higher battery Volt-Ampere-hour rating will mean you have more energy in the battery and can go further on your bike.
All of the above implies that both cases have the same energy efficiency which is not always true - motor controllers and other circuitry can have different efficiencies on different bike models. You should get details on the specific models you compare and pick the one you like more.
From my electrical theory days way back in my distant youth , higher voltages have less transmission losses for the same amount of power. But higher voltages come with the issue that they need better insulators. Lower voltages need larger conductors because for the same power level they need more current (amps, I)
This is all to do with : Volts = V = I * R = Amps * Ohms and Watts = I * I * R
All electrical circuits have resistance , impedance (AC resistance) . In theoretically ideal circuits the power is only dispipated in the load.
In realistic circuits power is disipated in the load and the power source. This is because the power source has an internal resistance.
So higher voltages mean less amps for the same power level. So there should be less power losses internal resistance of the power source and the cables transmitting the power, and thus more of the power gets dispipated in the load.
This is a bit of a simplified explanation.
Electrical circuits are a trade of between conductor size, insulation size, and safe voltages (that don't fry people).