SIXTY YEARS AGO.

We didn't know it at the time, but the United States won the race to the Moon in earth orbit.  As kids, we commemorated the event using a plastic mosaic tile playset.

Gerhard "Everyman Commentary" Thielmann offers a more technical explanation of the importance of rendezvous and docking and how it worked.

Before Apollo could land on the lunar surface, several operations needed to be accomplished. Specifically, suits had to enable an astronaut to function beyond the spacecraft’s protective envelope, approach and docking had to be reliably performed, and tolerance of cramped confinement needed medical assessment in order to determine whether an arduous transit to lunar orbit and return could be feasible.

None of these were easy to carry off.  Project Gemini, using cramped spacecraft capable of extended time in space, and each mission worked on one or more of those operations.  Approach and docking?  That's not intuitive.  To catch up, you slow down and go low.  "Decades prior, yours truly sat utterly bewildered in a class on orbital mechanics—at least until the radial rate equations finally made some non-intuitive sense."

What we did with our play set looked like this in real life.

National Aeronautics and Space Administration photo retrieved from Everyman Commentary.

Physically docking two spacecraft came later.

Subsequent Gemini flights the following year eventually achieved docking, and further improved activities outside the spacecraft. These flights included Gemini missions VIII, X, XI and XII, together with multiple spacewalks. Malfunction of a substitute target cancelled the scheduled docking operation for Gemini IX-A, but still permitted the completion of other tasks. Together, the Gemini missions enabled America to refine spacecraft design and operations, thereby paving the way for more ambitious goals.

Although Moon expeditions have not taken place for over fifty years, rendezvous, docking, and extravehicular activity are regular practice transporting astronauts to the space station.