Of a narrative, the quality that events are related according to an obvious ordering principle, especially time sequence.
In a work of Interactive Fiction, linearity is a metric of how many 'paths' exist from the beginning of the work to an optimal ending. A totally linear work would have only one possible path. (Consequently, only one winning walkthrough would exist). More conventionally, a game is said to be linear if, at any time, there is exactly one action that will advance the narrative in a significant way.
It is generally considered more difficult to produce a highly linear game which provides a satisfactory level of interactivity. However, it is likewise difficult to produce a highly alinear game which offers a coherent narrative or plot.
-- LRR 7-30-02