On is the name used for a particular combinatorial game that ensures at least a draw for one of its players.
In a combinatorial game, the two players, Left and Right, take turns making moves. If a player is called upon to make a move, but has no legal move, then that player loses.
In the game On, the Left player has one legal move, to pass. The Right player has no legal moves.
So Left can pass on every move and thus always has a legal move and cannot lose.
If Right has the move to pass, the game is instead called Off. If both Left and Right can pass, the game is called Dud.
On can be written diagrammatically as {On|}, where the On before the pipe indicates that Left has the ability to move to On, while the empty space after the pipe indicates that Right has no legal moves.