CAPCOM is an abbreviation for "Capsule Communicator." It is a term used by NASA to describe a specific Flight Controller position for NASA manned spaceflight missions. Starting with the first NASA manned spaceflight of Alan Shepard in the Freedom 7 spacecraft on May 5, 1961, NASA operations procedures dictated that all voice communications with astronauts in space must be either performed or controlled by a single person. That person is designated CAPCOM, and their callsign on all voice transmissions is the now-iconic "Houston" - so the familiar "Apollo, Houston..." phrase indicates that CAPCOM is beginning a transmission to an Apollo spacecraft.
Through the end of the Space Shuttle Program, CAPCOM was always a trained astronaut as NASA believed that that would help maximize understanding between ground and the spacecraft, which might be critical in emergencies. As of 2011, however, non-astronauts have begun filling in as CAPCOM for ISS duties. On longer flights, flight controllers work in shifts, and each shift has its own CAPCOM.
Note that CAPCOM is not the team leader at flight control. That position is held by the Flight Director, known as FLIGHT (as in, "Go, FLIGHT!" during countdowns).
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