Project Mercury was the first human spaceflight program of the United States. It ran from 1959 through 1963 with the goal of putting a human in orbit around the Earth. The Mercury-Atlas 6 flight on February 20, 1962, was the first American flight to achieve this goal. (image source)
The program included 20 unmanned launches, followed by two suborbital and four orbital flights with astronaut pilots. Early planning and research were carried out by the National Advisory Committee for Aeronautics (NACA), but the program was officially conducted by its successor organization, NASA. Mercury laid the groundwork for Project Gemini and the follow-on Apollo moon-landing program.
The project name came from Mercury, a Roman mythological god often seen as a symbol of speed. Mercury is also the name of the innermost planet of the Solar System, which moves faster than any other and hence provides an image of speed, although Project Mercury had no real connection to the planet.
Sources: wikipedia.org, infographicslibrary.com