Expository Narration is when the GM quickly describes several events in solid terms of fact without any interaction between them and the PCs. By tradition the PCs are usually expected to keep quiet and to not interrupt this GM information dump. That’s because when gaming was young (and all games were D&D mods) Boxed Text was used by the writers of those mods to setup each scene. Often they maneuvered the PCs, who could be anywhere and doing anything when a given scene began, into the position where the mod author assumed they would be for the sake of continuity. This way the reactions of the NPCs and environment would make sense.
For example, suppose your PCs opened a door in a dungeon. The boxed text may read something like “You open the door and a great gust of air sweeps you through it depositing the group in the center of a large chamber. Behind you the door slams closed and the sound reverberates off of the cold stone of this room you find yourself in.”
See what that Boxed Text did? The PCs chose to open the door. They did not however choose to rush into the room and blindly confront whatever happened to be on the other side. The author, however probably had in mind something happening in that room that the PCs would flee from if they had the chance. So instead of thinking of a way to convince the PCs to enter, they simply forced the decision. This is an excellent example of when not to use Expository Narration.
Put simply, you should never use Expository Narration in place of a PC decision.
The whole point of playing an RPG is the freedom of decision making. Your Players could just read a book to get a good story without having to make the important decisions. The reason they are interested in RPGing is so that they can be the ones making those decisions. If, as a GM, you take away that ability (even just once) you are making your own game pointless because there is no point to playing an RPG where the decision making is taken out of the PCs hands. First of all, what the PCs choose to do is the important thing here (regardless of what story the GM desires to tell). Besides if you aren’t imaginative or attentive enough to think of a way to sweeten the pot such that the PCs will choose to enter the room of their own free will in spite of the danger you probably shouldn’t be GMing.
How about this one? The PC, following a running thief, comes to a dark alley, debates turning back, and decides to press on (see the decision made?). Enter Boxed Text: “You proceed down the alley. About half way through it you hear a scuttling, scurrying sound. You try to turn and see where the sound is coming from when suddenly there is a sharp pain at the back of your neck and everything goes dark.”
What’s wrong with that one? PC decided to go down the alley, didn’t they? Well I’ll tell you what was wrong: something bad happened to your PC without them having any say in the matter. They should have gotten a roll. Really, what’s the point of putting all these numbers down on paper and buying all these dice if when it really counts, you don’t get to use them?
If they failed the roll to notice the person sneaking up on them and then the roll to avoid unconsciousness when that person did whatever it was they did, fine. They should have at least gotten the chance to try though. A good rule of thumb is that nothing bad should ever happen to a PC in Expository Narration. Those are the very situations in which they should get to participate. Taking that participation away, once again, removes the point of going through this story in RPG form rather than just reading a book.
Hard to overcome difficulties on the rolls or big penalties are one thing. You can make it unlikely that the PC will succeed at a given task (that’s not hard, you are the GM after all), but you have to give them the possibility of winning through and be willing to pay out if they do. People stop going back to the casino where all the tables are obviously rigged. There needs to be a certain amount of obvious winning going on to keep people interested. The same is true of a good game. Things can be stacked against the PCs, but they should, number 1, win more often than not and, number 2, should never lose without actually getting to spin the wheel. Not ever.
Oh and I know there will be some GMs who will decide that if, in the context of the story, the PC getting knocked out was “for their own good” it’s okay for the GM to give themselves a pass in this area. That is incorrect. Even if that PC in the example above wakes up at a friend’s house (the assumption being that getting knocked out wasn’t really a “bad” thing) the ultimate outcome does not matter at all. In this instance of Boxed Text, the PC still lost without even getting to roll some dice and let fate decide. Therefore this rule still applies.
When should Expository Narration be used, you ask?
For trivial things. It should be used to hurry your story forward through unimportant events. If the PCs become fixated on something that you honestly can’t think of a damn thing to do with, resolve it with some Boxed Text so the PCs know they should drop it and focus elsewhere. Use Boxed Text to jump forward a few weeks to the next big point of interest in the story. There is no reason to plod through the boring day-to-day lives of your PCs. Even if what their doing is interesting, if it has no real culmination or relation to the larger story, explain how it progresses week to week (or month to month depending on the game) rather than day by day so your game doesn’t get stale. That is what Expository Narration is for: blurring the passage of time in-game so all you ever spend your out-of-game time on is the creamy nougat of RPGing.