Syn- (= same as the Latin "con-") + kathistó (= "sat down") =
= Synkasthistó (i.e. "sitting in company").

In other words, such songs are not for dancing to, but for singing while sat at the table, perhaps after the meal, or between courses, or during a respite from dancing.

The term is equivalent to "epitrapezio" (from epi="on" or "at" and trapezi = "table"), i.e. "songs of the table".