A ghost runner is an imaginary player use to fill out a too-small baseball team.
Ghost runners have no official status in baseball. They are used primarily by children playing pickup games. Baseball teams should officially have nine members on each team, but few pickup games can muster this many players. Even if you have only four members on a team you can still play a decent game. If you fall below this number, ghost runners may be called into play. Judicious use of ghost runners may allow even two individuals to play a game of baseball.
After the batter has hit the ball (but failed to make a home run), he can declare that there is a ghost runner on the base he reached, and return to the plate for another go at bat. This ghost runner is a place holder that will automatically advance bases under certain conditions. Rules vary, but generally the ghost runner will not try to steal a base; instead it will advance one base for every base that the batter advances after hitting the ball again. Generally the ghost runner is exactly as fast as the person at bat, so he reaches his next base at the same time as the batter. (This is important, because if you don't know exactly where an invisible person is, it's very hard to tag them out.)
Ghost players can be used in other games, such as kickball. They should not be attempted in sports like soccer and tag, which require more spontaneity from their players. If you use ghost runners, always determine the rules governing them in advance! You simply cannot trust the other team to use their ghost runners responsibly unless you have a sound rule system established. Trust me on this.
This writeup was written with the help of The new Dickson baseball dictionary, by Paul Dickson.