Short answers, pulled from the story.
Earth orbit rendezvous is a method for conducting round trip human flights to the Moon by assembling, and possibly fueling, components of a translunar vehicle in low Earth orbit using space rendezvous and docking techniques. The two main proposed approaches were in-space assembly of fueled spacecraft modules and in-space refueling of fully assembled spacecraft.
NASA rejected EOR because it required a spacecraft large enough to make the full round trip from Earth orbit to the lunar surface and back. Lunar orbit rendezvous, the chosen alternative, allowed engineers to design a much smaller specialized lander that only needed to travel between lunar orbit and the surface.
Gemini 6 and Gemini 7 rendezvoused in orbit in 1965, and Gemini 8 became the first to successfully dock with an Agena target vehicle on the 16th of March, 1966. Later missions including Gemini 10, Gemini 11, and Gemini 12 demonstrated docked orbital maneuvering and spacewalks using the Agena.
Under Project Constellation, the Ares V rocket would launch the Earth Departure Stage and the Altair lunar lander into low Earth orbit, where they would be joined by the separately launched Orion crew vehicle. The combined stack would then travel to the Moon, with Orion and Altair flying a lunar orbit rendezvous pattern at the Moon itself.
Project Constellation was cancelled in October 2010, ending the program's planned use of Earth orbit rendezvous. The Ares V rocket and the Altair lunar lander were never flown.
American analysts in 1965 believed Earth orbit rendezvous was the preferred approach adopted by the Soviet Union for achieving human lunar missions, though this reflected American assessment rather than confirmed Soviet confirmation.