The key to high-energy stages was to use liquid hydrogen as the fuel.  Liquid hydrogen fuel appealed to rocket designers because of its high specific impulse, which is a basic measure of rocket performance. Specific Impulse is the impulse delivered per unit of propellant consumed.  You might think of it as the efficiency of the rocket.  Compared to an RP-1 (kerosene) fueled engine of similar size, liquid hydrogen fuel could increase the specific impulse or efficiency of an engine by 40 percent.  The combination of hydrogen and oxygen for propellants made the moon shot feasible.