The original plan was to fly a rocket all the way to the moon and land the complete rocket on the surface. This was indeed the plan for quiet some time, but how do you land a huge rocket on the moon, how would the astronauts get out of the 70 ft rocket and how much fuel would be needed to take off again ? One man at NASA had a different Idea, his name was John Houbolt but not being one of the main engineering team he struggled to get his voice heard. It was Houbolt that formulated the idea for a craft that would shuttle to the moon while the mother ship stayed in orbit, then the craft could return and dock with the mother ship.
But Wernher von Braun was the NASA expert on rockets and the face of the Apollo project, he was married to the Full rocket landing approach and cast Houbolt and his ideas aside. But with the full rocket idea not looking feasible Houbolt went over von Braun's head to Bob Seamans an Associate Administrator. Houbolt feared this action could get him fired but while Seamans was unsure he decided to at least let Houbolt present his idea for consideration.
In the documentary we see how von Braun eventually came around to the Lunar Excursion Module (LEM) idea. We meet with the people at Grumman Aircraft tasked with making the Lunar Module. And the enormous part the Lunar Excursion Module played in the Apollo missions from the first Moon landing module called The Eagle to the Apollo 13 mission when the module was used to save the lives of the three astronauts aboard.
