This is a baseball term which refers to base runners already on base when a relief pitcher is called in to play. These runners got on base while the previous pitcher was pitching, so any runs they score would be counted in the previous pitchers statistics. These runners do not count against the relief pitcher because he/she "inherited" them from the previous pitcher. This is an important distinction because the number of runs a pitcher is responsible for is paramount in the calculation of many important statistics which measure their effectiveness and efficiency.
Even though any runs scored by runners left on base by the previous pitcher do not count against the relief pitcher, a lot of teams and statistics databases count the number of base runners the relief pitcher inherited, and how many of them scored. It should be noted that if two, or even three previous pitchers each left a person on base, none of the runners would be the responsibility of the next pitcher brought it. Pitchers are only responsible for runs scored if the player got on base during their time on the mound.