The left stop and right stop (the stops) of a game in CGT are the first numbers reached by optimal play when Left or Right starts respectively. More broadly, the stopping positions of a game are simply all positions that are numbers. We also say that a game stops when play reaches a number.
The stops are the numbers provided by minimax applied to the left and right side of the game respectively.
In go terms, assume a board position is finished with when it is pure territory for Black and White. That leaves out who then has sente (important both for go and for CGT). It also leaves out ko threats, which isn't an aspect of go directly modelled in CGT.