A sanitation ship is a vessel in the Fleet.
Judging by its name, it can be assumed that it handles the sanitation needs for the Fleet.
After Athena joins Starbuck on the Rising Star, he asks the maitre d' for another private dining room, claiming that a sanitation ship could be seen popping in and out of view, which did not make for "appetizing scenery" (TOS: "The Long Patrol").