The writer's die was created by Daniel Solis as an aid to creating more interesting plots in stories and story-based games.
Daniel has an excellent, and comprehensive PDF guide for these dice, which give rules for how these can be used in many different ways in a range of story-based and role-playing games.
One simple use has a player roll the die after they've taken an action, or told part of the story. The result asks them to further elaborate, in a particular way. So rolling 'but' means they have to tell you something else that happens which contrasts in fortunes with their original event. Rolling 'and' requires a non-contrasting event. Rolling 'so' requires a consequence, 'or' needs a consequence, 'as' makes something happen at the same time, and 'if' makes it contingent.
The faces of the writer's die also have pips on them, so the die can be used as a regular d6. You need to be clear you're going to use the writer's die before you roll, however. You can't just choose it when you see it has a better result than the regular green d6!
You can visit Daniel's site here, and buy physical Writer's dice through his Etsy store. The dice design is used here with Daniel's permission.