After Project Mercury and before the Apollo missions, NASA needed to solve problems and practice for what they would need to do for successful flights to the moon. Thus the effort named Gemini moved things forward with two-person crews. What things? The ability to exit a spacecraft, as depicted above. Also to work in a weightless environment. For later missions beyond Earth orbit spacecraft would need to meet in space. Without that skill, moonwalkers would be stranded in deep space with no way home.
The US Postal Service issued a stamp in the mid-1960s to commemorate the ten missions that preceded the beginning of the Saturn rocket launches in 1967. It was the first time a “twin” stamp like this was produced. When used for regular letters, you just chose one side or the other: the astronaut or his Gemini spacecraft.
I don’t recall if I ever had one of these blocks-of-two. I might have demurred splitting them up; breaking that “umbilical” cord just would have seemed wrong.
Events during the project factored in to the selection of Neil Armstrong and Buzz Aldrin for the first moon landing. Armstrong was well-regarded for coolness under pressure when he saved Gemini 8 from tragedy. Aldrin for his research, work, and success in finally mastering tasks outside a space capsule in the Gemini 12 mission.