A bag or sac.
[Greek askos, a bag or wineskin.]
In botany, an ascus (plural ascii) is a sac in which the spores of ascomycete fungi develop (Greek mukētes, fungi), and the prefix can refer to this sac, as in ascospore for one of the spores it holds. In medicine, ascites is the accumulation of fluid in the peritoneal cavity, causing abdominal swelling.
Some words in asc- do not belong here: ascetic comes from another Greek word, askein, to exercise; others, such as ascertain and ascend, contain a variant form of ad-.