A linear game is one in which the GM intends a series of encounters in order, similar to the plot of a novel. Due to the interactive nature of RPGs, however, a linear game may fork from the original plan.
Linear games have the advantages of providing a succinct experience, allowing the GM to explore themes and situations in more detail, and satisfying traditional storytelling desires. It has the disadvantage of limiting individual choices, reducing spontaneity, and causing overpreparation trying to anticipate a number of possible outcomes. In a broken game, railroading may occur.
The opposite of a sandbox game, where the PCs largely decide what they get to do. In a linear game, the story is fairly programmatic, proceeding from one anticipated event to another.