Short answers, pulled from the story.
Lunar orbit rendezvous is a method for landing humans on the Moon in which a main spacecraft stays in lunar orbit while a separate lander descends to the surface. After the surface mission, the lander returns to lunar orbit, docks with the main craft, and only the main spacecraft makes the trip back to Earth. The chief advantage is that heavy return-trip propellant does not need to be carried to the surface and lifted back up.
Ukrainian engineer Yuri Kondratyuk first proposed lunar orbit rendezvous in 1919, describing it as the most economical method for a round-trip crewed journey to the Moon. Wernher von Braun and Heinz-Hermann Koelle later presented the concept to NASA leadership in December 1958.
Langley Research Center engineer John C. Houbolt was the most persistent advocate. In November 1961 he bypassed normal channels and wrote a nine-page private letter directly to NASA associate administrator Robert C. Seamans arguing that LOR was the only feasible way to reach the Moon by the end of the decade. NASA Administrator James Webb officially approved LOR in July 1962, with the decision announced at a press conference on the 11th of July, 1962.
Space rendezvous had never been achieved even in Earth orbit when LOR was being debated in 1962. If the lunar lander failed to dock with the waiting command module, two astronauts would be stranded in lunar orbit with no way to return to Earth. Rendezvous was successfully demonstrated on six Project Gemini missions in 1965 and 1966.
An oxygen tank explosion on Apollo 13 disabled the Command Module's systems in 1970. Because the Lunar Module carried its own independent electrical power, life support, and propulsion, the crew was able to use it as a lifeboat to survive and return safely to Earth. This backup capability had been anticipated as a contingency but was never formally written into the LEM specifications.
The proposed Soviet lunar landing program using the N1 rocket and LK Lander would have used a similar LOR profile. NASA's Artemis program plans to use rendezvous in a near-rectilinear halo orbit near the Moon to reach the lunar south pole. China's crewed lunar program, targeting 2029 or 2030, has also described a lunar landing mission using lunar orbit rendezvous.