Gemini spacecraft 6A and 7 rendevous in orbit. (NASA)
Gemini was the third manned spaceflight program undertaken by the United States of America, though it was completed before the second such program (Apollo). Conducted during the years 1963-1966, its goal was to develop techniques for advanced space travel, notably those necessary for the Apollo program, which was to land men on the Moon.
Gemini was originally seen as a simple extrapolation of the Mercury program and thus early on was called Mercury Mark II. The final program had little in common with Mercury and was in fact superior to even Apollo in some ways. This was mainly a result of its late start date, which allowed it to benefit from much that had been learned on Apollo up to that point.
Unlike Mercury, the Gemini capsule could alter its own orbit. It could also dock with other spacecraft--one of which, the Agena Target Vehicle, had its own large rocket engine which was used to perform large orbital changes. Gemini was the first American manned spacecraft to include an onboard computer, the Gemini Guidance Computer, to facilitate management and control of mission maneuvers.
The Gemini designation comes from the fact that the spacecraft held two men.
Gemini 6 views Gemini 7, 1965 (NASA)