Baseball term, for current
baserunners when a
relief pitcher is brought into the game. These runners got on base when the previous pitcher was in the game, so if they score, they would be credited to that previous pitcher.
As with many sports terms, it's hard to explain, so let me give an example. In today's Yankees/Cubs game, Yankees' pitcher Roger Clemens was winning 1-0 in the 7th inning, but 2 Cubs hitters got on base. The Yankees replaced Clemens with Juan Acevedo. Therefore, the 2 baserunners were "inherited" by Acevedo (since they reached base when Clemens was pitching). Acevedo then gave up a 3-run home run to Eric Karros, scoring both inherited runners. Those two runs are credited to Clemens (despite him not even being in the game when they scored). Karros's run is credited to Acevedo, of course.
Inherited runners are a fairly new term and not as mainstream as stolen bases or slugging percentage. However, the stat "percent of inherited runners scored" (or similar) is increasingly cited and is seen as an important to middle relievers. Afterall, if a pitcher enters the game with the bases loaded and gives up 2 hits that score all 3 inherited runners, his ERA might not be affected (since they're not "his" runners), but it's obviously a major negative that he let the runners score.
Noding note: Also referred to as "inherited baserunner". However a quick Yahoo search of "inherited baserunner" revealed 5 results; "inherited runner" produced 360 results. Therefore, am noding this under the more common usage, rather than the more "official" one.