A pass stone is a stone handed to the opponent as a captive when passing.
In AGA rules:
On his or her turn, a player may pass by handing the opponent a stone, referred to as a pass stone, rather than playing a stone on the board.
(copied from passing) Under most sets of rules a pass is free. However, under AGA rules of territory scoring a pass costs 1 point. The passer hands his opponent a stone as a captive, called a pass stone. Two consecutive passes end play, but White makes the last pass. The practical effect of pass stones is to reconcile territory and area scoring. Several people have had the idea of pass stones, but the AGA incorporation of them can be traced back to an American Go Journal article I wrote in the 1970s on the Chinese rules in which I called them bookkeeping stones. Pass stones sounds better, doesn't it? --Bill Spight